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現代数学の系譜11 ガロア理論を読む17 [転載禁止]©2ch.net

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>>54
> >>53 つづき
> 
> totally bounded >>52
> 
> https://en.wikipedia.org/wiki/Totally_bounded_space
> Totally bounded space
> 
> In topology and related branches of mathematics, a totally bounded space is a space that can be covered by finitely many subsets of any fixed "size" (where the meaning of "size" depends on the given context).
> The smaller the size fixed, the more subsets may be needed, but any specific size should require only finitely many subsets.
> A related notion is a totally bounded set, in which only a subset of the space needs to be covered. Every subset of a totally bounded space is a totally bounded set; but even if a space is not totally bounded, some of its subsets still will be.
> 
> Definition for a metric space
> A metric space (M,d) is totally bounded if and only if for every real number ε >0, there exists a finite collection of open balls in M of radius ε whose union contains M .
> Equivalently, the metric space M is totally bounded if and only if for every ε >0, there exists a finite cover such that the radius of each element of the cover is at most ε.
> This is equivalent to the existence of a finite ε-net.[1]
> 
> 参考 日wiki
> https://ja.wikipedia.org/wiki/%E5%85%A8%E6%9C%89%E7%95%8C%E7%A9%BA%E9%96%93
> 全有界空間
> 
> 位相幾何学および関連する数学の分野において、全有界空間（ぜんゆうかいくうかん、英: totally bounded space）とは、・・・

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