Talk:Compact space: Difference between revisions
Jump to navigation
Jump to search
imported>Wojciech Świderski |
imported>Jitse Niesen (→Compact set vs compact space: comment) |
||
| Line 8: | Line 8: | ||
:The terms ''compact set'' and ''compact space'' mean almost the same to me. Could you please explain the difference? -- [[User:Jitse Niesen|Jitse Niesen]] 09:33, 12 July 2008 (CDT) | :The terms ''compact set'' and ''compact space'' mean almost the same to me. Could you please explain the difference? -- [[User:Jitse Niesen|Jitse Niesen]] 09:33, 12 July 2008 (CDT) | ||
::In general, a compact set is part of surrounding topological space that may not be compact - as closed and bounded subsets of R^n. Compact space is "compact in itself" - we don't think of it as of part of something greater. Compact manifold is a good example - if you don't consider it as embedded in anything else. See: [http://mathworld.wolfram.com/CompactSpace.html] [[User:Wojciech Świderski|Wojciech Świderski]] 03:10, 13 July 2008 (CDT) | ::In general, a compact set is part of surrounding topological space that may not be compact - as closed and bounded subsets of R^n. Compact space is "compact in itself" - we don't think of it as of part of something greater. Compact manifold is a good example - if you don't consider it as embedded in anything else. See: [http://mathworld.wolfram.com/CompactSpace.html] [[User:Wojciech Świderski|Wojciech Świderski]] 03:10, 13 July 2008 (CDT) | ||
:::Okay, then we're using the same definitions. I was a bit surprised by your statement that "compact space" is more general than "compact set", but I guess it depends on how you look at it. Anyway, feel free to extend the discussion in the article. I do believe that "compact space" and "compact set" mean more or less the same (at least, the definitions are the same). Every compact set can be viewed as a compact space, if you forget about the space it's embedded in; every compact space is also a compact set in the space itself. So I think it's best to discuss both concepts in the same article. -- [[User:Jitse Niesen|Jitse Niesen]] 16:19, 13 July 2008 (CDT) | |||
Revision as of 15:19, 13 July 2008
Compact set vs compact space
Don't you think this article should be rather a subsection in more general compact space? Wojciech Świderski 05:28, 12 July 2008 (CDT)
- The terms compact set and compact space mean almost the same to me. Could you please explain the difference? -- Jitse Niesen 09:33, 12 July 2008 (CDT)
- In general, a compact set is part of surrounding topological space that may not be compact - as closed and bounded subsets of R^n. Compact space is "compact in itself" - we don't think of it as of part of something greater. Compact manifold is a good example - if you don't consider it as embedded in anything else. See: [1] Wojciech Świderski 03:10, 13 July 2008 (CDT)
- Okay, then we're using the same definitions. I was a bit surprised by your statement that "compact space" is more general than "compact set", but I guess it depends on how you look at it. Anyway, feel free to extend the discussion in the article. I do believe that "compact space" and "compact set" mean more or less the same (at least, the definitions are the same). Every compact set can be viewed as a compact space, if you forget about the space it's embedded in; every compact space is also a compact set in the space itself. So I think it's best to discuss both concepts in the same article. -- Jitse Niesen 16:19, 13 July 2008 (CDT)