Wikipedia:Reference desk/Archives/Mathematics/2021 May 25
Mathematics desk | ||
---|---|---|
< May 24 | << Apr | May | Jun >> | Current desk > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
May 25
editsufficient condition for two set to be sepreate-able (topology)
editHi,
I look for a sufficient condition that for the next claim to hold;
Let A be a compact subset
and let B1 and B2 two different connected component.
So there are 2 Open subset
1. 2. 3. 4.
Thanks!--Exx8 (talk) 19:01, 25 May 2021 (UTC)
- Is there supposed to be some relation between and the pair , or are all three just given? --Lambiam 23:44, 25 May 2021 (UTC)
- B1 and B2 are connected component of A.--Exx8 (talk) 05:14, 26 May 2021 (UTC)
- No additional conditions are necessary. The statement is true as given.--2406:E003:855:9A01:74B0:C329:6D75:B8CD (talk) 06:49, 26 May 2021 (UTC)
- Can you prove it?--Exx8 (talk) 12:52, 26 May 2021 (UTC)
- Is it true that the connected components of a compact space are all open? If so, one can take --Lambiam 08:43, 27 May 2021 (UTC)
- No. The connected components of the Cantor middle third set are the singletons.2406:E003:855:9A01:6D91:C1FE:E529:AA45 (talk) 00:00, 28 May 2021 (UTC)
- Is it true that the connected components of a compact space are all open? If so, one can take --Lambiam 08:43, 27 May 2021 (UTC)
- Can you prove it?--Exx8 (talk) 12:52, 26 May 2021 (UTC)
- @Exx8 Maybe this is equivalent to saying the components are all bounded away from each other- that is, given any two components there is some such that whenever and . Staecker (talk) 11:32, 28 May 2021 (UTC)
- Not equivalent (consider ) but the implication goes the right direction. --JBL (talk) 13:28, 28 May 2021 (UTC)