Talk:Clopen set

From Wikipedia, the free encyclopedia

You have new messages (last change).

This doesn't make much sense. Perhaps an example of a clopen set might make the idea comprehensible ? Theresa knott 06:46 25 May 2003 (UTC)

If you look at the articles on Open sets and Closed sets, you will find examples of Clopen sets. Perhaps some of them could be added to this article but if so it would only be repeating what exists elsewhere. -- Derek Ross 07:07 25 May 2003 (UTC)

[edit] Any clopen set is a union of (possibly infinitely many) connected components

This is trivial: since {x} is connected (in any Hausdorff space), then any clopen set is the union of all its elements: A = \bigcup_{x \in A} { \{ x \} } \,.

Should the text be Any clopen set is a union of (possibly infinitely many) connected clopen components?

I don't think this is true: \mathbb{Q}\, a likely counterexample. Albmont 15:56, 8 December 2006 (UTC)

Retrieved from "http://en.wikipedia.org../../../c/l/o/Talk%7EClopen_set_5bc3.html"