Baire category theorem: Difference between revisions
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In [[general topology]], the '''Baire category theorem''' states that a non-[[empty set|empty]] [[complete metric space]] is a [[second category space]]: that is, it is not a [[countability|countable]] [[union]] of [[nowhere dense set]]s (sets whose [[closure ( | In [[general topology]], the '''Baire category theorem''' states that a non-[[empty set|empty]] [[complete metric space]] is a [[second category space]]: that is, it is not a [[countability|countable]] [[union]] of [[nowhere dense set]]s (sets whose [[closure (topology)|closure]] have empty [[interior (topology)|interior]]). | ||
==References== | ==References== | ||
* {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=200-201 }} | * {{cite book | author=J.L. Kelley | authorlink=John L. Kelley | title=General topology | publisher=van Nostrand | year= 1955 | pages=200-201 }} | ||
Revision as of 15:31, 6 January 2009
In general topology, the Baire category theorem states that a non-empty complete metric space is a second category space: that is, it is not a countable union of nowhere dense sets (sets whose closure have empty interior).
References
- J.L. Kelley (1955). General topology. van Nostrand, 200-201.