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In topology, a CW complex is a type of topological space introduced by J. H. C. Whitehead to meet the needs of homotopy theory. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation (often with a much smaller complex). ==Formulation== Roughly speaking, a ''CW complex'' is made of basic building blocks called ''cells''. The precise definition prescribes how the cells may be topologically ''glued together''. The ''C'' stands for "closure-finite", and the ''W'' for "weak topology". An ''n''-dimensional closed cell is the image of an ''n''-dimensional closed ball under an attaching map. For example, a simplex is a closed cell, and more generally, a convex polytope is a closed cell. An ''n''-dimensional open cell is a topological space that is homeomorphic to the ''n''-dimensional open ball. A 0-dimensional open (and closed) cell is a singleton space. ''Closure-finite'' means that each closed cell is covered by a finite union of open cells. A CW complex is a Hausdorff space ''X'' together with a partition of ''X'' into open cells (of perhaps varying dimension) that satisfies two additional properties: * For each n-dimensional open cell ''C'' in the partition of ''X'', there exists a continuous map ''f'' from the ''n''-dimensional closed ball to ''X'' such that * * the restriction of ''f'' to the interior of the closed ball is a homeomorphism onto the cell ''C'', and * * the image of the boundary of the closed ball is contained in the union of a finite number of elements of the partition, each having cell dimension less than n. * A subset of ''X'' is closed if and only if it meets the closure of each cell in a closed set. 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「CW complex」の詳細全文を読む スポンサード リンク
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