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1. Grothendieck Topology - Wikipedia, The Free Encyclopedia
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://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 . A category together with a choice of Grothendieck topology is called a site 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 étale 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 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

2. Grothendieck Topology
Grothendieck topology 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
http://www.fact-index.com/g/gr/grothendieck_topology.html
Main Page See live article Alphabetical index
##### Grothendieck topology
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 schemess , but also for flat cohomology and crystalline cohomology. Note that a Grothendieck topology is not a topology in the classical sense.
##### 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 schemess . 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.
##### Motivating example
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

3. Wapedia - Wiki: 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://wapedia.mobi/en/Grothendieck_topology
 Wiki: 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 . A category together with a choice of Grothendieck topology is called a site 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 étale 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 rigid analytic geometry There is a natural way to associate a site to an ordinary topological space sobriety , this is completely accurate—it is possible to recover a sober space from its associated site. However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies. Conversely, there are Grothendieck topologies which do not come from topological spaces.

 4. Grothendieck Topology - Discussion And Encyclopedia Article. Who Is Grothendieck Grothendieck topology. Discussion about Grothendieck topology. Ecyclopedia or dictionary article about Grothendieck topology.http://www.knowledgerush.com/kr/encyclopedia/Grothendieck_topology/

5. Grothendieck Topology - Wikivisual
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.
http://en.wikivisual.com/index.php/Grothendieck_topology
Francais English
##### Grothendieck topology
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 Alexandre Grothendieck to define the étale cohomology of a scheme . It has been used to define many 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 Grothendieck topologies are not comparable to the classical notion of a topology on a space. While it is possible to interpret sober spaces in terms of Grothendieck topologies, more pathological spaces have no such representation. Conversely, not all Grothendieck topologies correspond to topological spaces.

6. Grothendieck Topology - Definition
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
http://www.wordiq.com/definition/Grothendieck_topology
##### Grothendieck topology - Definition
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). Contents showTocToggle("show","hide") 1 History and idea
2 Motivating example

3 Formal definition

4 Beyond cohomology
##### 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 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.
##### Motivating example
Start with a topological space X and consider the sheaf of all continuous real-valued functions defined on

7. Science Fair Projects - Grothendieck Topology
The Ultimate Science Fair Projects Encyclopedia Grothendieck topology
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Grot
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##### Grothendieck topology
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 �tale 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). Contents showTocToggle("show","hide")

 8. Grothendieck Topology | TripAtlas.com 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.http://tripatlas.com/Grothendieck_topology

 9. Grothendieck Topology A selection of articles related to Grothendieck topology Grothendieck topology Encyclopedia Site. A site is the location of an event or object, whether actual, virtual, or planned.http://www.experiencefestival.com/grothendieck_topology

 10. Grothendieck Topology : Define, Explore, Discuss Grothendieck topology Define, Explore, Discuss images, discuss, define, news.http://www.museumstuff.com/learn/topics/Grothendieck_topology

 11. Grothendieck Topology In Encyclopedia Grothendieck topology in Encyclopedia in Encyclopediahttp://www.tutorgig.com/ed/Grothendieck_topology

12. Grothendieck Topology - Wikipedia@pedia
Grothendieck topologyIn 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://wikipedia.atpedia.com/en/articles/g/r/o/Grothendieck_topology.html
wikipedia＠pedia wikipedia@PEDIA is study site of the language based on Wikipedia. TOP
##### Translation
Select text and it is translated. to AFRIKAANS to ALBANIAN to AMHARIC to ARABIC to ARMENIAN to AZERBAIJANI to BASQUE to BELARUSIAN to BENGALI to BIHARI to BULGARIAN to BURMESE to CATALAN to CHEROKEE to CHINESE to CROATIAN to CZECH to DANISH to DHIVEHI to DUTCH to ENGLISH to ESPERANTO to ESTONIAN to FILIPINO to FINNISH to FRENCH to GALICIAN to GEORGIAN to GERMAN to GREEK to GUARANI to GUJARATI to HEBREW to HINDI to HUNGARIAN to ICELANDIC to INDONESIAN to INUKTITUT to ITALIAN to JAPANESE to KANNADA to KAZAKH to KHMER to KOREAN to KURDISH to KYRGYZ to LAOTHIAN to LATVIAN to LITHUANIAN to MACEDONIAN to MALAY to MALAYALAM to MALTESE to MARATHI to MONGOLIAN to NEPALI to NORWEGIAN to ORIYA to PASHTO to PERSIAN to POLISH to PORTUGUESE to PUNJABI to ROMANIAN to RUSSIAN to SANSKRIT to SERBIAN to SINDHI to SINHALESE to SLOVAK to SLOVENIAN to SPANISH to SWAHILI to SWEDISH to TAJIK to TAMIL to TAGALOG to TELUGU to THAI to TIBETAN to TURKISH to UKRAINIAN to URDU to UZBEK to UIGHUR to VIETNAMESE This area is result which is translated word.

 13. Grothendieck Topology In - Dictionary And Translation Grothendieck topology. Dictionary terms for Grothendieck topology, definition for Grothendieck topology, Thesaurus and Translations of Grothendieck topology to English, Spanishhttp://www.babylon.com/definition/Grothendieck_topology/

14. 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://www.worldlingo.com/ma/enwiki/en/Grothendieck_topology
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##### Grothendieck topology
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##### 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 étale 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

15. Grothendieck Topology - On Opentopia, Find Out More About 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 set s of a topological space.
http://encycl.opentopia.com/term/Grothendieck_topology
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##### Grothendieck topology
Encyclopedia G GR GRO : 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 set s 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 Alexandre Grothendieck to define the étale cohomology of a scheme . It has been used to define many 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 Grothendieck topologies are not comparable to the classical notion of a topology on a space. While it is possible to interpret

 16. Grothendieck_topology Synonyms, Grothendieck_topology Antonyms | Thesaurus.com No results found for grothendieck_topology Please try spelling the word differently, searching another resource, or typing a new word. Search another word or seehttp://thesaurus.com/browse/Grothendieck_topology

17. 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, and with that the definition of