[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む17 [転載禁止]©2ch.net (747ﾚｽ)
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52(2): 現代数学の系譜11 ガロア理論を読む 2015/11/29(日)07:42 ID:SasjpBzo(1/14) AAS
>>50-51
どうも。スレ主です。
レスありがとう！
整いました（＾＾；

ルベーグ測度、μ(S) = 0 で合意します。

さて、本題
ルベーグ測度を確認すると、定義が「・・Rn の（高々）可算個の区間からなる区間族を総称して、Rn の区間塊という。」などと、非加算には直接使えない。外部ﾘﾝｸ:ja.wikipedia.org
省12

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53(2): 現代数学の系譜11 ガロア理論を読む 2015/11/29(日)08:02 ID:SasjpBzo(2/14) AAS
>>52
つづき
Every point of the Cantor set is also an accumulation point of the complement of the Cantor set.

For any two points in the Cantor set, there will be some ternary digit where they differ ? one will have 0 and the other 2.
By splitting the Cantor set into "halves" depending on the value of this digit, one obtains a partition of the Cantor set into two closed sets that separate the original two points.
In the relative topology on the Cantor set, the points have been separated by a clopen set. Consequently the Cantor set is totally disconnected. As a compact totally disconnected Hausdorff space, the Cantor set is an example of a Stone space.
引用おわり
省11

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54(3): 現代数学の系譜11 ガロア理論を読む 2015/11/29(日)08:44 ID:SasjpBzo(3/14) AAS
>>53 つづき

totally bounded >>52

外部ﾘﾝｸ:en.wikipedia.org
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.
省8

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