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Dense set
(Redirected from Dense (topology))
In topology and related areas of mathematics a subset of a topological space is called dense if the only closed subset of X containing A is X itself. This can also be expressed by saying that the closure of A is X. Equivalently, every nonempty open subset of X intersects A, or in other words: the interior of the complement of A is empty.
Examples
- every topological space is dense in itself
- the real numbers with the usual topology have the rational numbers and the irrational numbers as dense subsets
- a metric space space M is dense in its completion γM
See also
- separable space, a space with a countable dense subset
- nowhere dense set the opposite notion
10-26-2009 08:16:03
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The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details