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In mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. ==Motivation== Let ''X'' be a topological space, and let be an open cover of ''X''. Define a simplicial complex , called the nerve of the covering, as follows: * There is one vertex for each element of . * There is one edge for each pair such that . * In general, there is one ''k''-simplex for each ''k+1''-element subset of for which . Geometrically, the nerve is essentially a "dual complex" (in the sense of a dual graph, or Poincaré duality) for the covering . The idea of Čech cohomology is that, if we choose a "nice" cover consisting of sufficiently small open sets, the resulting simplicial complex should be a good combinatorial model for the space ''X''. For such a cover, the Čech cohomology of ''X'' is defined to be the simplicial cohomology of the nerve. This idea can be formalized by the notion of a good cover, for which every open set and every finite intersection of open sets is contractible. However, a more general approach is to take the direct limit of the cohomology groups of the nerve over the system of all possible open covers of ''X'', ordered by refinement. This is the approach adopted below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Čech cohomology」の詳細全文を読む スポンサード リンク
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