Stratification of a topological space: Difference between revisions

Latest revision as of 23:41, 24 October 2009

Definition

A stratification of a topological space $X$ is defined as a rule that associates, to each open subset $U$ of $X$ , a sequence ${U_{n}}_{n = 1}^{\infty}$ of open subsets, such that:

$\bar{U_{n}} \subset U$
$U = ⋃_{n = 1}^{\infty} U_{n}$
$U_{n} \subset V_{n}$ whenever $U \subset V$

A topological space which possesses a stratification is termed a stratifiable space.

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 ==Definition==
-A '''stratification''' of a [[topological space]] <math>X</math> is defined as a rule that associates, to each [[open subset]] <math>U</math> of <math>X</math>, a sequence <math>\{ U_n \}_{n=1}^\infty</math> of subsets, such that:
+A '''stratification''' of a [[topological space]] <math>X</math> is defined as a rule that associates, to each [[open subset]] <math>U</math> of <math>X</math>, a sequence <math>\{ U_n \}_{n=1}^\infty</math> of open subsets, such that:
 * <math>\overline{U_n} \subset U</math>