Talk:Clopen set

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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)

[edit] Standard terminology ?

I haven't heard of the term clopen set before; that's why I put the reference tag in the article. Can anyone state a reference ? Thanks. MP (talk•contribs) 20:21, 14 January 2008 (UTC)

Here are just a few of the textbooks mentioning this term:
http://www.amazon.com/s/ref=nb_ss_/002-0295115-4340819?url=search-alias%3Daps&field-keywords=clopen
I don't know where the term originated, but it pops up all over the place. Dcoetzee 23:17, 14 January 2008 (UTC)

[edit] Do we really need this section?

This is not a commen term. I think that it is one the terms rlm introduced. —Preceding unsigned comment added by 130.164.67.108 (talk) 09:49, 22 April 2008 (UTC)