1. Topology - Wikipedia, The Free Encyclopedia topology (Greek topos, place, and logos, study ) is a branch of mathematics that is an extension of geometry. topology begins with a consideration of the http://en.wikipedia.org/wiki/Topology

Topology From Wikipedia, the free encyclopedia Jump to: navigation search For other uses, see Topology (disambiguation) Not to be confused with topography A M¶bius strip , an object with only one surface and one edge; such shapes are an object of study in topology. Topology Greek topos , "place," and logos , "study") is a branch of mathematics that is an extension of geometry . Topology begins with a consideration of the nature of space, investigating both its fine structure and its global structure. Topology builds on set theory , considering both sets of points and families of sets. The word topology is used both for the area of study and for a family of sets with certain properties described below that are used to define a topological space . Of particular importance in the study of topology are functions or maps that are homeomorphisms . Informally, these functions can be thought of as those that stretch space without tearing it apart or sticking distinct parts together. When the discipline was first properly founded, toward the end of the 19th century , it was called geometria situs Latin geometry of place ) and analysis situs Latin analysis of place ). From around 1925 to 1975 it was an important growth area within mathematics.

2. Topology -- From Wolfram MathWorld topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. http://mathworld.wolfram.com/Topology.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Forfar Topology Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed. A circle is topologically equivalent to an ellipse (into which it can be deformed by stretching) and a sphere is equivalent to an ellipsoid . Similarly, the set of all possible positions of the hour hand of a clock is topologically equivalent to a circle (i.e., a one-dimensional closed curve with no intersections that can be embedded in two-dimensional space), the set of all possible positions of the hour and minute hands taken together is topologically equivalent to the surface of a torus (i.e., a two-dimensional a surface that can be embedded in three-dimensional space), and the set of all possible positions of the hour, minute, and second hands taken together are topologically equivalent to a three-dimensional object. The definition of topology leads to the following mathematical joke (Renteln and Dundes 2005): Q: What is a topologist? A: Someone who cannot distinguish between a doughnut and a coffee cup.

3. What Is Topology? An introductory essay by Neil Strickland, University of Sheffield. http://neil-strickland.staff.shef.ac.uk/Wurble.html

What is topology? Topologists are mathematicians who study qualitative questions about geometrical structures. We do not ask: how big is it? but rather: does it have any holes in it? is it all connected together, or can it be separated into parts? A commonly cited example is the London Underground map. This will not reliably tell you how far it is from Kings Cross to Picadilly, or even the compass direction from one to the other; but it will tell you how the lines connect up between them. In other words, it gives topological rather than geometric information. Again, consider a doughnut and a teacup, both made of BluTack. We can take one of these and transform it into the other by stretching and squeezing, without tearing the BluTack or sticking together bits which were previously separate. It follows that there is no topological difference between the two objects. Consider the problem of building a fusion reactor which confines a plasma by a magnetic field. Imagine a closed surface surrounding the plasma. At each point on the surface, the component of the magnetic field parallel to the surface must be nonzero, or the plasma will leak out. We are thus led to the following question: given a surface S, is it possible for there to be a field of vectors tangent at each point of S which is nowhere zero? It turns out that this depends solely on the topological nature of S. If S is the surface of a sphere, it is not possible. Magnetic confinement of a ball of plasma just does not work. The only type of surface for which this approach is possible is the inner tube shape, which is of course the solution universally used for such reactors. (I do not claim that engineers needed topologists to point this out; on the contrary, this is a nice example precisely because many people can see for themselves that the claim is true.) Another amusing consequence of the same argument is that at any given time, some point on the Earth's surface is windless.

4. Topology - Elsevier topology publishes papers in many parts of mathematics, but with special emphasis on subjects which are related to topology or geometry, such as http://www.elsevier.com/locate/top

Home Site map Elsevier websites Alerts ... Topology Journal information Product description Audience Abstracting/indexing Special issues and supplements ... Peer review Policy Subscription information Bibliographic and ordering information Conditions of sale Dispatch dates Journal-related information Contact the publisher Impact factor Most downloaded articles Other journals in same subject area ... Select your view TOPOLOGY Most Downloaded Articles Description Topology publishes papers in many parts of mathematics, but with special emphasis on subjects which are related to topology or geometry, such as: Topology publishes survey articles. Only papers of the highest quality appear in this journal. ISSN: 0040-9383 Imprint: ELSEVIER Commenced publication 1962 Subscriptions for the year 2008, Volume 47, 6 issues Personal price: Order form USD 104 for all countries except Europe, Japan and Iran JPY 13,800 for Japan EUR 104 for European countries and Iran Institutional price: Order form USD 1,665 for all countries except Europe, Japan and Iran JPY 197,700 for Japan

5. Topology History Topological ideas, concepts and functional analysis. http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Topology_in_mathematics.h

A history of Topology Geometry and topology index History Topics Index Version for printing Topological ideas are present in almost all areas of today's mathematics. The subject of topology itself consists of several different branches, such as point set topology, algebraic topology and differential topology, which have relatively little in common. We shall trace the rise of topological concepts in a number of different situations. Perhaps the first work which deserves to be considered as the beginnings of topology is due to Euler . In 1736 Euler published a paper on the solution of the entitled Solutio problematis ad geometriam situs pertinentis which translates into English as The solution of a problem relating to the geometry of position. The title itself indicates that Euler was aware that he was dealing with a different type of geometry where distance was not relevant. Here is The paper not only shows that the problem of crossing the seven bridges in a single journey is impossible, but generalises the problem to show that, in today's notation, A graph has a path traversing each edge exactly once if exactly two vertices have odd degree.

6. Topology Atlas Preprints, abstracts, calendar, links, other resources. http://at.yorku.ca/topology/

Topology Atlas is a publisher of information related to topology. What's New Search Preprints Abstracts ... About Topology Atlas Favorites: Topology Q+A Board Upcoming Conferences Topology Proceedings Lecture Notes

7. Course 212 - Topology The lecture notes for course 212 (topology), taught at Trinity College, Dublin, in the academic year 20002001, are available here. http://www.maths.tcd.ie/~dwilkins/Courses/212/

Course 212 - Topology The lecture notes for course 212 ( Topology ), taught at Trinity College, Dublin, in the academic year 2000-2001, are available here. The course consists of three parts:- Part I: Limits and Continuity, Open and Closed Sets, Metric Spaces DVI PDF PostScript Part II: Topological Spaces DVI PDF PostScript Part III: Normed Vector Spaces and Functional Analysis DVI PDF PostScript Part IV: Topology in the Plane DVI PDF PostScript dwilkins@maths.tcd.ie ... Trinity College , Dublin 2, Ireland dwilkins@maths.tcd.ie

8. What Is Topology? Basically, topology is the modern version of geometry, the study of all different sorts of spaces. The thing that distinguishes different kinds of geometry http://www.math.wayne.edu/~rrb/topology.html

What is Topology? A short and idiosyncratic answer Robert Bruner Basically, topology is the modern version of geometry, the study of all different sorts of spaces. The thing that distinguishes different kinds of geometry from each other (including topology here as a kind of geometry) is in the kinds of transformations that are allowed before you really consider something changed. (This point of view was first suggested by Felix Klein, a famous German mathematician of the late 1800 and early 1900's.) In ordinary Euclidean geometry, you can move things around and flip them over, but you can't stretch or bend them. This is called "congruence" in geometry class. Two things are congruent if you can lay one on top of the other in such a way that they exactly match. In projective geometry, invented during the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. For example, look at a plate on a table from directly above the table, and the plate looks round, like a circle. But walk away a few feet and look at it, and it looks much wider than long, like an ellipse, because of the angle you're at. The ellipse and circle are projectively equivalent. This is one reason it is hard to learn to draw. The eye and the mind work projectively. They look at this elliptical plate on the table, and think it's a circle, because they know what happens when you look at things at an angle like that. To learn to draw, you have to learn to draw an ellipse even though your mind is saying `circle', so you can draw what you really see, instead of `what you know it is'.

9. Mathematics Archives - Topics In Mathematics - Topology In the Mathematics Archives at University of Tennessee, Knoxville. http://archives.math.utk.edu/topics/topology.html

Topics in Mathematics Topology Algebraic and Geometric Topology ADD. KEYWORDS: Electronic and printed journal SOURCE: TECHNOLOGY: Postscript and Adobe Acrobat PDF Reader Algebraic Topology ADD. KEYWORDS: Textbook, Homotopy and Homotopy Type, Cell Complexes, Fundamental Group and Covering Spaces, Van Kampen's Theorem, Homology, Cohomology, Poincare Duality, Universal Coefficient Theorem, Homotopy Groups, Hopf Invariant Algebraic Topology Discussion List ADD. KEYWORDS: Newsgroup, meetings, people AMS's Materials Organized by Mathematical Subject Classification - Algebraic Topology ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification - General Topology ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification - Manifolds and Cell Complexes ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMS's Materials Organized by Mathematical Subject Classification - Topological Groups and Lie Groups ADD. KEYWORDS:

10. Algebraic Topology Book A complete, downloadable, introductory text on Algebraic topology, by Prof. Allen Hatcher, Cornell Univ. 3rd Ed. 553 pp. with illustrations. http://www.math.cornell.edu/~hatcher/AT/ATpage.html

Algebraic Topology What's in the Book? To get an idea you can look at the Table of Contents and the Preface Printed Version The book was published by Cambridge University Press in 2002 in both paperback and hardback editions, but only the paperback version is currently available (ISBN 0-521-79540-0). This is now in a seventh printing. Each printing contains corrections of various minor errors not yet weeded out from the earlier printings see farther down this page for a list of corrections. I have tried very hard to keep the price of the paperback version as low as possible, but it is gradually creeping upward and is now $34 in the US. Less expensive printings have been made for sale in China (Tsinghua University Press) and South Asia. A translation into Russian is underway. Electronic Version: By special arrangement with the publisher, an online version will continue to be available for free download here, subject to the terms in the . There are several different formats available: The whole book as a single rather large pdf file (3.5MB) of about 550 pages.

11. The Math Forum - Math Library - Topology The Math Forum s Internet Math Library is a comprehensive catalog of Web sites and Web pages relating to the study of mathematics. This page contains sites http://mathforum.org/library/topics/topology/

Browse and Search the Library Home Math Topics : Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Algebraic Topology Knot Theory Topological Groups/Lie Groups Selected Sites (see also All Sites in this category GN General Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis General Topology preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives. Search by keyword or browse by topic. more>> Investigating Patterns: R-U-B-B-E-R Geometry (Topology) - Jill Britton Selected web pages for educators, each leading to recreation-oriented learning experiences for middle school students. Topics include: Topology / Anamorphic Art; Jordan Curves / Mazes / Networks / Map Coloring; Math-e-Magic / Mobius Strip; Flexagons.  more>> The Topological Zoo - The Geometry Center For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each object is accompanied by a short description that provides background information and interconnections among the objects in the zoo. Where appropriate, the equations that describe the objects are included. Primarily a reference, not an introduction to topology or other branches of mathematics. An ongoing project at the Geometry Center, the work of graduate students from the the University of Minnesota and undergraduates who participate in the Summer Institute at the Geometry Center.

12. Topology She’s working on a new bunch of songs for topology, which we’ll play together, along with some new and favourite instrumentals by ourselves. http://www.topologymusic.com/

Topology 3 April New podcast - Composers Talking Composers Talking powered by ODEO Tags: prosody skyhooks red symons composition composers inter Posted in Composers 29 March Drums, anyone? Brisbane Powerhouse and Topology present Sun 13 Apr 08 Sell-out sensation and one-man percussion orchestra, Grant Collins, meets musical adventurers Topology to take rhythm into uncharted territory and push the limits of musical possibility. Master of his one-tonne drumkit, Grant Collins has teamed up with the multi-award winning contemporary chamber ensemble, Topology. In a one-night musical escapade, punctuated by the visceral energy of this exciting new collaboration, the fearsome polyrhythms of Grant’s originals will explode with Topology’s intense mix of strings, sax and piano. “It’s hard to imagine a human acoustic drumkit performer advancing much beyond this level” US Drum Magazine (on Grant Collins) Book Online More info Tags: collaboration crossover drums polyrhythm ... rhythm Posted in Concerts 8 March Facebook Topology page Posted in Concerts 7 February Restrung! 28 Feb - 2 Mar (starting now!)

13. Geometry Topology, Volume 12 (2008) A fully refereed international journal dealing with all aspects of geometry and topology and their applications. Full text free. Articles are deposited in http://www.msp.warwick.ac.uk/gt/

14. What Is Topology? - A Definition From Whatis.com A topology (from Greek topos meaning place) is a description of any kind of locality in terms of its layout. In communication networks, a topology is a http://searchnetworking.techtarget.com/sDefinition/0,,sid7_gci213156,00.html

mboxCreate('global'); topology Home Networking Definitions - Topology SearchNetworking.com Definitions (Powered by WhatIs.com) EMAIL THIS LOOK UP TECH TERMS Powered by: Search listings for thousands of IT terms: Browse tech terms alphabetically: A B C D ... Z topology Digg This! StumbleUpon Del.icio.us ttWriteMboxDiv('searchNetworking_Definition_Body'); ttWriteMboxContent('searchNetworking_Definition_Body'); - A topology (from Greek topos meaning place) is a description of any kind of locality in terms of its layout. In communication networks, a topology is a usually schematic description of the arrangement of a network, including its nodes and connecting lines. There are two ways of defining network geometry: the physical topology and the logical (or signal) topology. The physical topology of a network is the actual geometric layout of workstations. There are several common physical topologies, as described below and as shown in the illustration. In the bus network topology, every workstation is connected to a main cable called the bus . Therefore, in effect, each workstation is directly connected to every other workstation in the network.

15. Crystallographic Topology The topology of Crystallographic Groups and Simple Crystal Structures. http://www.ornl.gov/ortep/topology.html

Crystallographic Topology The Topology of Crystallographic Groups and Simple Crystal Structures Carroll K. Johnson Michael N. Burnett Oak Ridge National Laboratory Australian Mirror Site UK Mirror Site Preprints and Presentations Crystallographic Topology 101 - A Tutorial / Virtual Course 1. Overview 2. Introduction to Orbifolds 2.1. Elliptic 2-Orbifolds from Point Groups 2.2. Euclidean 2-Orbifolds from Plane Groups 3. Introduction to Critical Nets 4. Critical Nets on Orbifolds ... Orbifold Atlas under construction Cubic Space Group Orbifolds What's New (Mar. 15, 1999) Colleagues and Their Abstracts Related Web Sites ... ORTEP-III Computer Program Send comments, questions, suggestions, etc. to: topology@ornl.gov Oak Ridge National Laboratory Home Page Page last revised:

16. Topology s and illustrations of several topological and differential geometry related notions....... http://www.chez.com/alcochet/toposi.htm

TOPOLOGY Here are fundamental objects of the lacanian topology : The Möbius band The torus The Klein bottle The cross-cap The borromean knot Topology is a branch of pure mathematics, deals with the fundamental properties of abstract spaces. Whereas classical geometry is concerned with measurable quantities, such as angle, distance, area, and so forth, topology is concerned with notations of continuity and relative position. Point-set topology regards geometrical figures as collections of points, with the entire collection often considered a space. Combinatorial or algebraic topology treats geometrical figures as aggregates of smaller building blocks. BASIC CONCEPTS In general, topologists study properties of spaces that remain unchanged, no matter how the spaces are bent, stretched, shrunk, or twisted. Such transformations of ideally elastic objects are subject only to the condition that nearby points in one space correspond to nearby points in transformed version of that space. Because allowed deformation can be carried out by manipulating a rubber sheet, topology is sometimes known as rubber-sheet geometry. In contrast, cutting, then gluing together parts of a space is bound to fuse two or more points and to separate points once close together. The basic ideas of topology surfaced in the mid-19th century as offshoots of algebra and ANALYTIC GEOMETRY. Now the field is a major mathematical pursuit, with applications ranging from cosmology and particle physics to the geometrical structure of proteins and other molecules of biological interest.

17. Webopedia: Network Topologies topology refers to the shape of a network, or the network s layout. How different nodes in a network are connected to each other and how they communicate http://www.webopedia.com/quick_ref/topologies.asp

You are in the: Small Business Computing Channel ECommerce-Guide Small Business Computing Webopedia ... Refer-It Enter a word for a definition... ...or choose a computer category. choose one... All Categories Communications Computer Industry Companies Computer Science Data Graphics Hardware Internet and Online Services Mobile Computing Multimedia Networks Open Source Operating Systems Programming Software Standards Types of Computers Wireless Computing World Wide Web Home Term of the Day New Terms Pronunciation ... Quick Reference Network Topologies Topology refers to the shape of a network , or the network's layout. How different nodes in a network are connected to each other and how they communicate are determined by the network's topology. Topologies are either physical or logical . Below are diagrams of the five most common network topologies. Mesh Topology Devices are connected with many redundant interconnections between network nodes . In a true mesh topology every node has a connection to every other node in the network. Star Topology All devices are connected to a central hub . Nodes communicate across the network by passing data through the hub. Bus Topology All devices are connected to a central cable, called the

18. Hopf Topology Archive, Revised Version Algebraic topology and related areas. (~400 articles) http://hopf.math.purdue.edu/

Hopf Topology Archive Welcome to the Hopf Topology Archive! NOTICE: Hopf has been moved to a virtual website on the Math department server. Most things should be transparent if you use http://hopf.math.purdue.edu as the URL. The FTP service will not be reactivated due to security concerns. If you experience problems, please report them to wilker@math.purdue.edu Thank you. Hopf Author/Title Search: enter author or title keyword into box below. PaperSearch The Hopf Logos The Hopf Archive, month by month listing. This archive list is current through August 2004 . Newer files may be in the proper directories but not listed on the html list. These are accessible as http://hopf.math.purdue/AuthorName <- usually last names of authors. If you have a submission that has not been announced or posted and some time has elapsed, please email Mark and Clarence (but please try the "Reload" button on your browser first. Thanks, Clarence) What's New! CW-Fest: MidWest Topology Seminar honoring Clarence Wilkerson's 60th birthday. Submitting Preprints and Uploading Preprints Latest maintained by Mark Hovey. Back issues of Mark's What's New!

19. Topology - Wikibooks, Collection Of Open-content Textbooks General topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, http://en.wikibooks.org/wiki/Topology

Topology From Wikibooks, the open-content textbooks collection Jump to: navigation search Contents Introduction Before You Begin Point - Set Topology Some Set Theory ... edit Introduction General Topology is based solely on set theory and concerns itself with structures of sets. It is at its core a generalization of the concept of distance, though this will not be immediately apparent for the novice student. Topology generalises many distance related concepts, such as continuity, compactness and convergence. For an overview of the subject of topology, please see the Wikipedia entry edit Before You Begin In order to make things easier for you as a reader, as well as for the writers, you will be expected to be familiar with a few topics before beginning. (I hope to have some links to other Wikibooks here soon.) Real analysis Continuous Functions Set Theory Set Operations: Union, Intersection, Complement, De Morgan's laws , etc. Order Relations : Ordered Sets, Equivalence relations, Lattices Functions: Definition and Properties of Functions Cardinality : Finite, Countable, and Uncountable sets

20. Pearson - Topology, 2/E For a senior undergraduate or first year graduatelevel course in Introduction to topology. Appropriate for a one-semester course on both general and http://www.pearsonhighered.com/academic/product/0,,0131816292,00+en-USS_01DBC.ht

/*********************************************** * Tab Content script- © Dynamic Drive DHTML code library (www.dynamicdrive.com) * This notice MUST stay intact for legal use * Visit Dynamic Drive at http://www.dynamicdrive.com/ for full source code ***********************************************/ About Pearson Higher Education Search our catalog: Browse by discipline or Anthropology Art English History ... Exam copy bookbag Addison-Wesley / Prentice Hall Mathematics Browse available resources for Mathematics: Select a resource Resources for Mathematics ICTCM Instructor Resource Center myPearsonStore Pearson Tutor Services ... View larger cover Topology, 2/E James Munkres Massachusetts Institute of Technology ISBN-10: 0131816292 ISBN-13: 9780131816299 Publisher: Prentice Hall Format: Cloth; 537 pp Published: 12/28/1999 Suggested retail price: $128.80 Buy from myPearsonStore Request a printed exam copy Email this page to a colleague Prepare for the First Day of Class ... Next Edition(s) For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses. Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

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