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・ Topsfield
・ Topsfield (CDP), Massachusetts
・ Topsfield Town Common District
・ Topsfield, Maine
・ Topsfield, Massachusetts
・ Topsham
・ Topsham (CDP), Maine
・ Topsham Air Force Station
・ Topsham quarries
・ Topsham railway station
・ Topsham, Devon
・ Topsham, Maine
・ Topsham, Vermont
・ Topshelf Records
・ Toporów, Świętokrzyskie Voivodeship
Topos
・ Topos (disambiguation)
・ Topos de Reynosa FC
・ Topos de Tlatelolco
・ Toposa
・ Toposa language
・ Toposa people
・ Toposcope
・ Topotactic transition
・ TopoTarget
・ Topote
・ Topotecan
・ Topoteretes
・ Topothesia
・ Topovlje


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Topos : ウィキペディア英語版
Topos

In mathematics, a topos (, or ; plural topoi or , or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site). Topoi behave much like the category of sets and possess a notion of localization; they are in a sense a generalization of point-set topology. The Grothendieck topoi find applications in algebraic geometry; the more general elementary topoi are used in logic.
==Grothendieck topoi (topoi in geometry)==
Since the introduction of sheaves into mathematics in the 1940s a major theme has been to study a space by studying sheaves on a space. This idea was expounded by Alexander Grothendieck by introducing the notion of a "topos". The main utility of this notion is in the abundance of situations in mathematics where topological heuristics are very effective but an honest topological space is lacking; it is sometimes possible to find a topos formalizing the heuristic. An important example of this programmatic idea to date is the étale topos of a scheme.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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