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Zero-dimensional space : ウィキペディア英語版 | Zero-dimensional space
In mathematics, a zero-dimensional topological space (or nildimensional) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.〔(【引用サイトリンク】publisher=planetmath.org )〕 An illustration of a nildimensional space is a point. ==Definition== Specifically: * A topological space is zero-dimensional with respect to the Lebesgue covering dimension if every finite open cover of the space has a finite refinement which is a cover of the space by open sets such that any point in the space is contained in exactly one open set of this refinement. * A topological space is zero-dimensional with respect to the small inductive dimension if it has a base consisting of clopen sets. The two notions above agree for separable, metrisable spaces.
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「Zero-dimensional space」の詳細全文を読む
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