Difference between revisions of "Dense"

Latest revision as of 15:42, 18 August 2006

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Let $X$ be a topological space and $S$ be a subspace of $X$ . Then $S$ is dense in $X$ if, for any $x\in X$ and any open neighborhood $U\ni x$ , $U\cap S\neq\varnothing$ . For example, the rational numbers are dense in the real numbers.

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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 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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+Let <math>X</math> be a [[topological space]] and <math>S</math> be a [[subspace]] of <math>X</math>. Then <math>S</math> is '''dense''' in <math>X</math> 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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Difference between revisions of "Dense"

Latest revision as of 15:42, 18 August 2006