Development of a topological space: Difference between revisions

Latest revision as of 19:43, 11 May 2008

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Definition

Let $X$ be a topological space. A development for $X$ is a countable collection $F_{1},F_{2},\ldots$ of open covers of $X$ , such that for any closed subset $C\subset X$ and any point $p\notin C$ , there exists a $F_{j}$ such that no member of $F_{j}$ which contains $p$ intersects $C$ .

A topological space which has a development is termed a developable space.

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 ==Definition==
-Let <math>X</math> be a [[topological space]]. A '''development''' for <math>X</math> is a countable collection <math>F_1, F_2, \ldots</math> of [[open cover]]s of <math>X</math>, such that for any [[closed subset]] <math>C \subset X</math> and
+Let <math>X</math> be a [[topological space]]. A '''development''' for <math>X</math> is a countable collection <math>F_1, F_2, \ldots</math> of [[open cover]]s of <math>X</math>, such that for any [[closed subset]] <math>C \subset X</math> and any point <math>p \notin C</math>, there exists a <math>F_j</math> such that no member of <math>F_j</math> which contains <math>p</math> intersects <math>C</math>.
+A topological space which has a development is termed a [[developable space]].