Talk:Compact space: Difference between revisions
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imported>Jitse Niesen (what's the difference?) |
imported>Wojciech Świderski |
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: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) | |||
Revision as of 02:10, 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)