Talk:Boundary point: Difference between revisions

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imported>Peter Schmitt
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imported>Boris Tsirelson
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== every point is a boundary case ==
"...every point is a boundary case, or there is no boundary point at all — are both possible. In the first case the set is said to be dense in the space" — Really? The whole space is a (trivial) example of a dense set, but belongs to the latter case, not the former one. The condition "every point of the space is a boundary point of the given set" is equivalent rather to "the given set and its complement are both dense". [[User:Boris Tsirelson|Boris Tsirelson]] 09:18, 4 October 2009 (UTC)

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 Definition:  (of a set) In geometry and topology, a point such that every neighbourhood contains both points in the set and points not in the set. [d] [e]
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every point is a boundary case

"...every point is a boundary case, or there is no boundary point at all — are both possible. In the first case the set is said to be dense in the space" — Really? The whole space is a (trivial) example of a dense set, but belongs to the latter case, not the former one. The condition "every point of the space is a boundary point of the given set" is equivalent rather to "the given set and its complement are both dense". Boris Tsirelson 09:18, 4 October 2009 (UTC)

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