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Let ''X'' be a topological space and ''S'' a subspace. Then ''S'' is '''dense''' in ''X'' if, for any <math>x\in X</math> and any [[open]] neighborhood <math>U\ni x</math>, <math>U\cap S\neq\varnothing</math>. For example, the [[rational number]]s are dense in the [[real number]]s. | Let ''X'' be a topological space and ''S'' a subspace. Then ''S'' is '''dense''' in ''X'' if, for any <math>x\in X</math> and any [[open set|open]] neighborhood <math>U\ni x</math>, <math>U\cap S\neq\varnothing</math>. For example, the [[rational number]]s are dense in the [[real number]]s. | ||
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Revision as of 11:52, 10 July 2006
Let X be a topological space and S a subspace. Then S is dense in X if, for any 
and any open neighborhood 
, 
. For example, the rational numbers are dense in the real numbers.
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