For faster navigation, this Iframe is preloading the Wikiwand page for 一致性质.

一致性质

数学领域拓扑学中,一致性质一致不变性一致空间的在一致同构下不变的性质。

因为出现的一致空间是拓扑空间而一致同构是同胚,所有一致空间的所有拓扑性质都是一致性质。本文关心不是拓扑性质的一致性质。

一致性质

[编辑]
  • 分离。一致空间X分离的,如果所有周围的交集等于X×X中的对角。这实际上就是拓扑性质,并等价于底层拓扑空间是豪斯多夫空间(或简单的T0空间的条件,因为所有一致空间都是完全正则空间)。
  • 完备。一致空间X完备的,如果所有X中的柯西网收敛(就是说,有极限点X中)。
  • 完全有界(或预紧致)。一致空间X是完全有界的,如果对于每个周围EX×X,有X的有限覆盖{Ui}使得Ui×Ui对于所有的i被包含在E中。等价的说,X是完全有界的,如果对于每个周围E存在X的有限子集{xi}使得X是所有E[xi]的并集。依据一致覆盖,X是完全有界的,如果所有一致覆盖都有有限子覆盖。
  • 紧致。一致空间是紧致的,如果它是完备的并且完全有界的。尽管这里给出了定义,紧致性是拓扑性质并有纯粹拓扑描述(所有开覆盖都有有限子覆盖)。
  • 一致连通。一致空间X是一致连通的,如果所有从X离散一致空间一致连续函数都是常数的。
  • 一致不连通。一致空间X是一致不连通的,如果所有从离散一致空间到X的一致连续函数都是常数的。

参见

[编辑]

引用

[编辑]
{{bottomLinkPreText}} {{bottomLinkText}}
一致性质
Listen to this article

This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.
Please download and use one of the following browsers:

This article was just edited, click to reload
This article has been deleted on Wikipedia (Why?)

Back to homepage

Please click Add in the dialog above
Please click Allow in the top-left corner,
then click Install Now in the dialog
Please click Open in the download dialog,
then click Install
Please click the "Downloads" icon in the Safari toolbar, open the first download in the list,
then click Install
{{::$root.activation.text}}

Install Wikiwand

Install on Chrome Install on Firefox
Don't forget to rate us

Tell your friends about Wikiwand!

Gmail Facebook Twitter Link

Enjoying Wikiwand?

Tell your friends and spread the love:
Share on Gmail Share on Facebook Share on Twitter Share on Buffer

Our magic isn't perfect

You can help our automatic cover photo selection by reporting an unsuitable photo.

This photo is visually disturbing This photo is not a good choice

Thank you for helping!


Your input will affect cover photo selection, along with input from other users.

X

Get ready for Wikiwand 2.0 🎉! the new version arrives on September 1st! Don't want to wait?