1. Grothendieck Topology - Wikipedia, The Free Encyclopedia and Physical Sciences, 279 241342, Dordrecht Kluwer Academic Publishers Group. Retrieved from http//en.wikipedia.org/wiki/grothendieck_topology http://en.wikipedia.org/wiki/Grothendieck_topology

Grothendieck topology From Wikipedia, the free encyclopedia Jump to: navigation search In category theory , a branch of mathematics , a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space . Grothendieck topologies axiomatize the notion of an open cover . Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology . This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the ©tale cohomology of a scheme . It has been used to define other cohomology theories since then, such as l-adic cohomology flat cohomology , and crystalline cohomology . While Grothendieck topologies are most often used to define cohomology theories, they have found other applications as well, such as to John Tate 's theory of rigid analytic geometry There is a natural way to associate a category with a Grothendieck topology (a site ) to an ordinary topological space , and Grothendieck's theory is loosely regarded as a generalization of classical topology. Under meager point-set hypotheses, namely sobriety , this is completely accurate—it is possible to recover a sober space from its associated site. However simple examples such as the

2. Grothendieck Topology - Encyclopedia Article - Citizendium Retrieved from http//en.citizendium.org/wiki/grothendieck_topology . Categories CZ Live Mathematics Workgroup. Views. Article; Discussion; View source http://en.citizendium.org/wiki/Grothendieck_topology

We are creating the world's most trusted encyclopedia and knowledge base. The general public and experts collaborate, using their real names. Grothendieck topology From Citizendium, the Citizens' Compendium Jump to: navigation search Main Article Talk Related Articles Bibliography External Links This is a draft article , under development. These unapproved articles are subject to edit intro The notion of a Grothendieck topology or site' captures the essential properties necessary for constructing a robust theory of cohomology of sheaves. The theory of Grothendieck topologies was developed by Alexander Grothendieck and Michael Artin. Definition A Grothendieck topology T consists of A category, denoted c a t T A set of coverings , denoted c o v T , such that for each object U of c a t T If , and is any morphism in c a t T , then the canonical morphisms of the fiber products determine a covering If and , then Examples A standard topological space X becomes a category o p X when you regard the open subsets of X as objects, and morphisms are inclusions. An open covering of open subsets U clearly verify the axioms above for coverings in a site. Notice that a

3. Grothendieck Topology - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/grothendieck_topology.html . This page has been accessed 672 times. This page was last modified 1047, http://www.indopedia.org/Grothendieck_topology.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS Categories Category theory Sheaf theory Printable version ... Wikipedia Article Grothendieck topology ज्ञानकोश: - The Indological Knowledgebase In mathematics , a Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C , and with that the definition of general cohomology theories. A category together with a Grothendieck topology on it is called a site . This tool is used in algebraic number theory and algebraic geometry , mainly to define étale cohomology of schemes , but also for flat cohomology and crystalline cohomology . Note that a Grothendieck topology is not a topology in the classical sense. Contents showTocToggle("show","hide") 1 History and idea 2 Motivating example 3 Formal definition 4 Beyond cohomology ... edit History and idea At a time when cohomology for sheaves on topological spaces was well established, Alexander Grothendieck wanted to define cohomology theories for other structures, his schemes . He thought of a sheaf on a topological space as a "measuring rod" for that space, and the cohomology of such a measuring rod as a rough measure for the underlying space. His goal was thus to produce a structure which would allow the definition of more general sheaves or "measuring rods"; once that was done, the model of topological cohomology theories could be followed almost verbatim. edit Motivating example Start with a topological space X and consider the sheaf of all continuous real-valued functions defined on

4. Grothendieck Topology - Wikipedia Retrieved from http//nostalgia.wikipedia.org/wiki/grothendieck_topology . This page was last modified 0123, 4 December 2001. Content is available under http://nostalgia.wikipedia.org/wiki/Grothendieck_topology

Grothendieck topology From Wikipedia HomePage Recent changes View source Page history ... Log in Special pages Double redirects Broken redirects Disambiguation pages Log in Preferences My watchlist Recent changes Upload file File list Gallery of new files User list Statistics Random page Orphaned pages Uncategorized pages Uncategorized categories Uncategorized files Uncategorized templates Unused categories Unused files Wanted pages Wanted categories Most linked to pages Most linked to categories Most linked-to templates Pages with the most categories Most linked to files Pages with the most revisions Pages with the fewest revisions Short pages Long pages New pages Oldest pages Dead-end pages Protected pages Protected titles All pages Prefix index List of blocked IP addresses and usernames User contributions What links here Book sources Categories Export pages Version System messages Logs MIME search Search for duplicate files List redirects Unused templates Random redirect Pages without language links File path Search List of Wikimedia wikis Expand templates CategoryTree Gadgets Parser diff test Cross-namespace links Wikimedia Board of Trustees election Search web links Printable version A Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C , and with that the definition of general cohomology theories. A category together with a Grothendieck topology on it is called a

5. Grothendieck Topology - MathWiki $ /amsmath . If math is a sieve over math , and math , then math . Retrieved from http//mathwiki.gc.cuny.edu/index.php/grothendieck_topology http://mathwiki.gc.cuny.edu/index.php/Grothendieck_topology

Grothendieck topology From MathWiki edit Formal Definition A Grothendieck topology on a category is a function from the objects of to sets of sieves of such that The maximal sieve for all If , and , then , where is defined as the pullback WikiTeX: latex reported a failure, namely: This is TeX, Version 3.14159 (Web2C 7.4.5) (./a9e7899030c70c5b695aa36338da6331 LaTeX2e Babel $ l.28 ! Missing $ inserted. $ l.29 If is a sieve over , and , then Retrieved from " http://mathwiki.gc.cuny.edu/index.php/Grothendieck_topology Views Article Discussion Edit History Personal tools Create an account or log in Navigation Main Page Current events Courses Lectures ... Help Search Toolbox What links here Related changes Upload file Special pages ... Printable version This page was last modified 00:22, 12 July 2006. This page has been accessed 136 times. About MathWiki

6. Grothendieck Topology - ᏗᎪᏪᎵ ᎦᏧᎾᎳ Ꭶ Translate this page http//chr.wolfmountaingroup.com/wiki/grothendieck_topology . Topos theory Sheaf theory http://chr.wikigadugi.org/wiki/Grothendieck_topology

Grothendieck topology Grothendieck topology ᎨᏒᎢ structure (ᎠᏛᎯᏍᏙᏗ) ᏀᎾ ᎤᎾᏓᏟᏌᎲ C C topological ᎤᏜᏠᏛ . Grothendieck topologies axiomatize ᎦᎵᏓᏍᏛ . ᎬᏗᏍᎬᎢ ᎦᎵᏓᏍᏛ ᎫᏢᎥᏍᎬ ᎠᏓᏁᎳᏠᎾᎥᎢ Grothendieck topology, ᎾᏍᎩ becomes (ᏗᏙᎳᎩ) ᏰᎵᏊ ᎧᏁᎢᏍᏔᏠᎯ sheaves (ᎾᏍᎩ ᎠᎨᏴ ᎠᏎᎸᎯ) cohomology algebraic (ᏗᏎᏍᏗ) ᏗᏎᏍᏗ ᏓᏍᏓᏠᏠalgebraic (ᏗᏎᏍᏗ) ᏎᏍᏗ ᎪᎷᏩᏛᏗ ... ©tale cohomology . ᎾᏍᎩ ᎤᎭ ᏭᏪᏙᎢ ᎢᏯᏛᏁᎵᏓᏍᏗ ᎧᏁᎢᏍᏔᏠᎯ ᏐᎢ cohomology theories (ᎪᎷᏩᏛᏗ) ᎣᏂ ᏧᏩᎫᏛ ᏀᎢᏳᎢ, ᎤᏠᏱ l-adic cohomology ᎤᏩᎾᏕᏍᎩ cohomology crystalline (ᎠᎧᎵᏬᎯ) cohomology . ᏀᎢᏳᎢ Grothendieck topologies ᎢᏳᏓᎵᎭ ᎢᏯᏛᏁᎵᏓᏍᏗ ᎧᏁᎢᏍᏔᏠᎯ cohomology theories (ᎪᎷᏩᏛᏗ), ᎤᏠᏌ ᎤᎭ ᎠᏩᏛᏗ ᏐᎢ ᏗᏔᏲᏍᏙᏗ ᏥᏄᏍᏗ ᎠᏔᎴᏒ ᎠᎹᏱ, ᎤᏠᏱ ᏣᏂ Tate rigid (ᏗᏙᎳᎩ) analytic (ᏗᏎᏍᏗ) ᏗᏎᏍᏗ ᏓᏍᏓᏠᏠᎤᏚᎳᏗ ᏂᎬᏩᏍᏛ ᎦᎶᎯᏍᏗ ᎤᎾᎵᎪᎯ ᎤᎾᏓᏟᏌᎲ ᎬᏙᏗ Grothendieck topology ( site (ᏄᏍᏗᏓᏠ) topological ᎤᏜᏠᏛ , ᎠᎴ Grothendieck ᎪᎷᏩᏛᏗ ᎨᏒᎢ loosely (ᏗᏲᏒᎯ) ᎾᏍᎩ ᎠᏰᎸᏠᏥᏄᏍᏗ generalization (ᏂᎦᎥ) classical (ᎢᏧᎳᎭ ᏗᏂᏱᎴᎩ) topology. ᎭᏫᎾᏗᏢ ᎦᏲᎵ ᎪᏍᏓᏱ-ᎠᏫᏒᏗ hypotheses, ᏗᎪᎥᎯ

7. Grothendieck Topology Articles And Information Grothendieck topology. In mathematics,Grothendieck topology isstructure defined on an arbitrary category C which allowsdefinitionsheaves on C,with http://neohumanism.org/g/gr/grothendieck_topology.html

Current Article Grothendieck topology In mathematics Grothendieck topology isstructure defined on an arbitrary category C which allowsdefinition sheaves on C ,with thatdefinitiongeneral cohomology theories. A category together withGrothendieck topology on itcalled site . This toolused algebraic number theory algebraic geometry schemess , but alsoflat cohomologycrystalline cohomology. Note thatGrothendieck topologynot topology inclassical sense. Historyidea Attime when cohomologysheaves on topological spaces was well established, Alexander Grothendieck wanteddefine cohomology theoriesother structures, his schemess . He thought ofsheaf ontopological space as"measuring rod"that space, andcohomologysuchmeasuring rod asrough measure forunderlying space. His goal was thusproducestructure which would allowdefinitionmore general sheaves or "measuring rods"; once that was done,modeltopological cohomology theories could be followed almost verbatim. Motivating example Start withtopological space X considersheafall continuous real-valued functions defined on X . This associatesevery open set U X set F U )real-valued continuous functions defined on U . Whenver U issubset V , we have"restriction map" from F V F U ). If we interprettopological space

8. Grothendieck Topology A selection of articles related to Grothendieck topology. http://www.experiencefestival.com/grothendieck_topology

Articles Archives Start page News Contact Community General Newsletter Contact information Site map Most recommended Search the site Archive Photo Archive Video Archive Articles Archive More ... Wisdom Archive Body Mind and Soul Faith and Belief God and Religion ... Yoga Positions Site map 2 Site map Grothendieck topology A Wisdom Archive on Grothendieck topology Grothendieck topology A selection of articles related to Grothendieck topology More material related to Grothendieck Topology can be found here: Index of Articles related to Grothendieck Topology Grothendieck topology Page 2 ARTICLES RELATED TO Grothendieck topology Grothendieck topology: Encyclopedia II - Grothendieck topology - Definition See also: Grothendieck topology Grothendieck topology - Introduction Grothendieck topology - Definition Grothendieck topology - Sites and sheaves Read more here: Grothendieck topology: Encyclopedia - Alexander Grothendieck Alexander Grothendieck (born March 28, 1928) was one of the most important mathematicians active in the 20th century. He was also one of its most extreme scientific personalities, with achievements over a short span of years that are still scarcely credible in their broad scope and sheer bulk, and an approach that antagonised even close followers. He made major contributions to algebraic geometry, homological algebra, and functional analysis. He was awarded the Fields Medal in 1966, and co-awarded the Crafoord Prize with Pierre Delig ... Including: Alexander Grothendieck - Mathematical achievements Alexander Grothendieck - Major mathematical topics from R©coltes et Semailles Alexander Grothendieck - Life Alexander Grothendieck - Childhood and studies ... Alexander Grothendieck - Disappearance Read more here:

9. Grothendieck Topology Translate this page Updated Pages. date, page. Mar 01, model_category_defin Mar 01, model_category_defin Mar 01, differential_cohomol Mar 01, other_configurations.html http://pantodon.shinshu-u.ac.jp/topology/literature/Grothendieck_topology.html

Your language? Japanese English Mar, 2008 Sun Mon Tue Wed Thu Fri Sat Updated Pages date page Mar 31 von_Neumann_algebra.html Mar 31 Morse_theory.html Mar 30 A-infinity.html Mar 30 Morse_theory.html Mar 30 Floer_homotopy_type.html Mar 30 Floer_homology.html Mar 30 Morse_theory.html Mar 29 operad_related.html Mar 29 analytic_homology.html Mar 29 quasiabelian.html Mar 29 analytic_homology.html Mar 29 measure_theory.html Mar 29 analytic_homology.html Mar 29 geometric_homology.html Mar 29 geometric_homology.html Mar 28 Mar 27 Mar 27 toric_topology.html Mar 26 Mar 26 abelian_group.html objectives precautions index ... search Grothendieck Topology 手っ取り早く学ぶのなら Mac Lane と Moerdijk の本 か Kashiwara と Schapira の本 が良いのではないだろうか。 Vistoli の Vis Grothendieck topology を代数的トポロジーに使ったものとしては以下の仕事があ る。 Mark Johnson による spectrum や多重ループ空間 Hopf algebroid は affine groupoid scheme であり、 Hopf algebroid 上 の comodule はその groupoid scheme 上の quasi-coherent sheaf とみなせ る。 References Mark Hovey. Morita theory for Hopf algebroids and presheaves of groupoids.

10. Grothendieck_topology In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a http://pedia-site.com/Grothendieck_topology

Site Go to The Main Page Add Site to favorite! Grothendieck topology In category theory , a branch of mathematics , a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space . Grothendieck topologies axiomatize the notion of an open cover . Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology . This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the ©tale cohomology of a scheme . It has been used to define other cohomology theories since then, such as l-adic cohomology flat cohomology , and crystalline cohomology . While Grothendieck topologies are most often used to define cohomology theories, they have found other applications as well, such as to John Tate 's theory of rigid analytic geometry There is a natural way to associate a category with a Grothendieck topology (a site ) to an ordinary topological space , and Grothendieck's theory is loosely regarded as a generalization of classical topology. Under meager point-set hypotheses, namely sobriety , this is completely accurate—it is possible to recover a sober space from its associated site. However simple examples such as the

11. F) INTERESSANTE WEB-VERBINDUNGEN ZU VERSCHIEDENEN MATHEMATISCHEN grothendieck_topology Group_Theory Homological_Algebra Industrial_Math Integral_Equations Integral_Transforms KTheory Lattice Lie_Algebra Linear_Algebra http://www.ucy.ac.cy/~ddais/german/ms_ge.htm

F) I NTERESSANTE WEB-V ERBINDUNGEN ZU VERSCHIEDENEN MATHEMATISCHEN THEMEN Exemplarisch ausgew Allgemeine Verbindungen Number Theory Combinatorics Geometry Algebra ... Geometrynet GEOMETRY. NET... Algebra Arithematic Biostatistics Calculus ... Wavelets Algebrai sche Kurven im Internet Algebraic Curves (Geometry Center, Minnesota) Famous Curves Index (St. Andrews) The Cubic Surface Homepage (Mainz) Some pictures of algebraic curves (Minnesota) ... Projections of complex plane curves to real three-space Maple package for Algebraic Curves: examples and documentation Algebrai Acme Klein Bottles Algebraic surfaces Nice pictures from Bruce Hunt Animated algebraic surfaces Some very cool pictures of surfaces! Barth's sextic Fly through Barth's sextic Benno Artmann's Topological Models Boy's Surface Build your own Boy's surface out of paper! Boy Surface Some interesting information and pictures. Duncan's Mathematical Models Some gifs of surfaces and whatnot. Cubic Surface Models of cubic surface made out of paper/wood by a fourth grade class in Italy Enriques surfaces Description, examples, and some amazing pictures.

12. Grothendieck Topology - Mathematics Dictionary And Research Guide Wikipedia and Wikis. Grothendieck topology Wikipedia http//en.wikipedia.org/wiki/grothendieck_topology. Keywords and Synonyms http://www.123exp-math.com/t/01704058365/

The Language of Mathematics - Dictionary and Research Guide Provided by Search: Add to Favorites Grothendieck topology In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. Grothendieck topologies axiomatize the notion of an open cover. Wikipedia and Wikis Grothendieck topology - Wikipedia http://en.wikipedia.org/wiki/Grothendieck_topology Keywords and Synonyms Grothendieck topology, Grothendieck topos, Grothendieck site, Grothendieck topologies More topics about: Grothendieck topology Edit this page Add new links, rate and edit existing links, or make suggestions. - Staff Explore related topics: module ring Abelian group Yoneda lemma ... Category theory Some descriptions may have been derived in part from Princeton University WordNet or Wikipedia Last update: March 1, 2008

13. Tiny Wikipedia Dump Test Grosse_Tete,_Louisiana Grosser_garten Grosseto Grossraeschen Grote_Markt_/_GrandPlace grothendieck_topology Grotius Groton Groton,_Connecticut Groton http://facetroughgemstones.com/wikipedia/gr/

Office Supplies Buy Posters A-Z Products Website Advertising gr GR GRD GREEK GRID ... wikipedia.org 10 carat TOP Hot pink raspberry COBALTO DRUSY freeform wirewrap Druzy jewelry BEAUTIFUL 51 gram Hot Cherry very pink red RHODONITE Tumble polished cabbing 255 ct 4 gr Blue sheen flash shiller MOONSTONE feldspar Moon Stone ing jewel 25 carats Green PERIDOTS tumbled polished designer jewelry 5 grams PRETTY 9 gram MAHOGANY OBSIDIAN Cab lapidary carving tumbled polished Jewelry raw

14. Grothendieck_topology.html Grothendieck topology You have new messages (last change). In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category http://myplanet24.com/index.php?vc=2&visilex_key=Grothendieck_topology.html

15. Good Math, Bad Math : Big To Small, Small To Big: Topological Properties Through http//en.wikipedia.org/wiki/grothendieck_topology. In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C http://scienceblogs.com/goodmath/2006/12/big_to_small_small_to_big_topo.php

@import url(/seed-static/global.css); @import url(/seed-static/NEWNEW.css); @import url(http://www.seedmagazine.com/seed-static/inc/masthead.css); @import url(http://scienceblogs.com/goodmath/GM-BM-main.css/blog.css); Seed Media Group document.write(''); Latest Posts Archives About RSS ... Contact Search this blog Profile Mark Chu-Carroll (aka MarkCC) is a PhD Computer Scientist, who works for Google as a Software Engineer. My professional interests center on programming languages and tools, and how to improve the languages and tools that are used for building complex software systems. Other Information Recent Posts Introduction to Linear Regression Framing and Expelled: Why the Framers are Mis-Framing Basic Statistics: Mean and Standard Deviation Nim ... Meta out the wazoo: Monads and Monoids Recent Comments Dr Rick on Basic Statistics: Mean and Standard Deviation Bob O'H on Introduction to Linear Regression Ashwin Nanjappa on Basic Statistics: Mean and Standard Deviation Peter on Introduction to Linear Regression Earthceuticals on Introducing Game Theory Eduardo Mauro on Introduction to Linear Regression Torbj¶rn Larsson, OM on

16. $q - $host Retrieved from http//en.wikipedia.org/grothendieck_topology . Categories Topos theory Sheaf theory. This text is available under the terms of the GNU http://backup-reports.com/Grothendieck_topology

$host Search: Topics $keywords Visit also backup-reports.com gift-report.com health-notes.com insurance-notes.com ... stock-notes.com News $news Search the Web $wiki

17. Grothendieck Topology - Biocrawler grothendieck_topology. Retrieved from http//www.biocrawler. com/encyclopedia/grothendieck_topology . Categories Category theory Sheaf theory http://www.biocrawler.com/encyclopedia/Grothendieck_topology

Inline videos See also: Category: Articles with embedded Videos. Grothendieck topology From Biocrawler In mathematics , a Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C , and with that the definition of general cohomology theories. A category together with a Grothendieck topology on it is called a site This tool has been used in algebraic number theory and algebraic geometry , initially to define étale cohomology of schemes , but also for flat cohomology and crystalline cohomology , and in further ways. Note that a Grothendieck topology is a true generalisation. It is not a topology in the classical sense, and may not be equivalent to giving one (although it can be used to faithfully model sober spaces Table of contents showTocToggle("show","hide") 1 History and idea 2 Motivating example 3 Formal definition 4 Presheaves and sheaves ... edit History and idea See main article Background and genesis of topos theory At a time when cohomology for sheaves on topological spaces was well established, Alexander Grothendieck wanted to define cohomology theories for other structures, his

18. All Articles: Page 59 grothendieck_topology Groton Groton,_New_Hampshire Groton,_South_Dakota Groton,_Vermont Groton_Long_Point,_Connecticut Grottoes,_Virginia http://www.sparen-versicherung.de/everything-59.html

All Articles: Page 59 All Articles - Page 59 Pages: Greenockite Greenpeace Greenport,_Columbia_County,_New_York Greenport,_New_York ... Impressum

19. Grothendieck Topology Contents. Grothendieck topology. A Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C, http://www.ebroadcast.com.au/lookup/encyclopedia/gr/Grothendieck_topology.html

Make eBroadcast my Homepage Contact Us It's Web Guide Encyclopedia Contents Grothendieck topology A Grothendieck topology is a structure defined on an arbitrary category C which allows the definition of sheaves on C , and with that the definition of general cohomology theories. A category together with a Grothendieck topology on it is called a site . This tool is mainly used in algebraic geometry , for instance to define . Note that a Grothendieck topology is not a topology in the classical sense. The motivating example is the following: start with a topological space X and consider the sheaf of all continuous real-valued functions defined on X . This associates to every open set U in X the set F U ) of real-valued continuous functions defined on U . Whenver U is a subset of V , we have a "restriction map" from F V ) to F U ). If we interpret the topological space X as a category, with the open sets being the objects and a morphism from U to V if and only if U is a subset of V , then F is revealed as a contravariant functor from this category into the category of sets. In general, every contravariant functor from a category C to the category of sets is therefore called a pre-sheaf of sets on C . Our functor F has a special property: if you have an open covering ( V i ) of the set U , and you are given mutually compatible elements of F V i ), then there exists precisely one element of

20. Grothendieck Topologie Grothendieck topologie. V matematice, Grothendieck topologie je struktura definovaná na libovolný kategorie C který dovolí definici svazk na C, http://wikipedia.infostar.cz/g/gr/grothendieck_topology.html

švodn­ str¡nka Tato str¡nka v origin¡le Grothendieck topologie V matematice Grothendieck topologie je struktura definovan¡ na libovoln½ kategorie C kter½ dovol­ definici svazků na C , a s t­m definice gener¡la cohomology teorie. Kategorie spolu s Grothendieck topologie na tom je naz½v¡na m­stem . Tento n¡stroj je použ­v¡n v teorii algebraick©ho č­sla a algebraick© geometrii , hlavně vymezit ©tale cohomology schemess , ale tak© pro ploch© cohomology a krystalick© cohomology. Poznamenejte, že Grothendieck topologie nen­ topologie v klasick©m smyslu. Historie a n¡pad V době když cohomology pro svazky na topological prostorech byly dobře ustaven©, Alexander Grothendieck chtěl definovat cohomology teorie pro jin© struktury, jeho schemess . On myslel na svazek na prostoru topological jak “nivelačn­ lati” pro ten prostor a cohomology takov½ nivelačn­ laÅ¥ jako tvrd¡ m­ra pro z¡kladov½ prostor. Jeho c­l byl tak produkovat strukturu, kter¡ by dovolila definici v­ce svazků gener¡la nebo “nivelačn­ lati”; jednou to bylo děl¡no, model topological cohomology teori­ mohl b½t n¡sledov¡n t©měř doslovně. Motivovat př­klad Zač­nat prostorem topological X a zvažovat svazek vÅ¡ech spojit½ skutečn½-oceněn½ funkce vymezily na X . Toto st½k¡ se ke každ©mu otevřen©mu souboru U v X soubor F U ) skutečn½-oceněn© spojit© funkce vymezily na U . Whenver U je podmnožina V , my m¡me “mapu omezen­â€ od F V ) k F U ). Jestliže my interpretujeme prostor topological

Page 1     1-20 of 59    1  | 2  | 3  | Next 20