Talk:Compact space

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Revision as of 02:10, 13 July 2008 by imported>Wojciech Świderski (→‎Compact set vs compact space)
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 Definition:  A toplogical space for which every covering with open sets has a finite subcovering. [d] [e]
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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)
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