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Questions in category: 点集拓扑 (General Topology).

Precompact set

Posted by haifeng on 2011-07-24 10:09:33 last update 2023-07-26 11:08:50 | Answers (0) | 收藏

Precompact set 有几种解释

Relatively compact subspace (相对紧集), 也就是指闭包是紧的集合.
Totally bounded set (全有界集).
仿紧. (拓扑空间 $X$ 如果每个开覆盖都有一个局部有限的加细开覆盖(简称开加细), 则称 $X$ 是仿紧空间.[1])

References:

[1] 陆文钊、陈肇姜编著, 《点集拓扑学》南京大学出版社. 1995.

[2] Relatively-compact set - Encyclopedia of Mathematics