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Cosmic space : ウィキペディア英語版 | Cosmic space
In mathematics, particularly topology, a cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular ''T''1 spaces but not in general), a space is cosmic if and only if it has a countable network; namely a countable collection of subsets of the space such that any open set is the union of a subcollection of these sets. Cosmic spaces have several interesting properties. There are a number of unsolved problems about them. ==Examples and properties==
* Any open subset of a cosmic space is cosmic since open subsets of separable spaces are separable. * Separable metric spaces are trivially cosmic.
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「Cosmic space」の詳細全文を読む
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