| 翻訳と辞書 |
| axiom of countability ： ウィキペディア英語版 |
axiom of countability
In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that asserts the existence of a countable set with certain properties. Without such an axiom, such a set might not provably exist.
==Important examples==
Important countability axioms for topological spaces include:〔.〕
*sequential space: a set is open if every sequence convergent to a point in the set is eventually in the set
*first-countable space: every point has a countable neighbourhood basis (local base)
*second-countable space: the topology has a countable base
*separable space: there exists a countable dense subspace
*Lindelöf space: every open cover has a countable subcover
*σ-compact space: there exists a countable cover by compact 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「axiom of countability」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|