Weak fibration: Difference between revisions

Revision as of 19:09, 2 December 2007

This article defines a property of continuous maps between topological spaces

Definition

A continuous map $p : E \to B$ is termed a weak fibration or a Serre fibration if given any map $F : I^{n} \times I \to B$ and a map $\tilde{f} : I^{n} \to E$ such that $p (\tilde{f} (x)) = f (x, 0)$ , there exists a map $\tilde{F} : I^{n} \times I \to E$ satisfying:

$p \circ \tilde{F} = F$
$F (x, 0) = \tilde{f} (x)$

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 ==Definition==
-A [[continuous map]] <math>p:E \to B</math> is termed a '''weak fibration''' or a '''Serre fibration''' if given any map <math>F:I^n \times I \to B</math> and a map <math>\tilde{f}: X \to E</math> such that <math>p(\tilde{f}(x)) = f(x,0)</math>, there exists a map <math>\tilde{F}:I^n \times I \to E</math> satisfying:
+A [[continuous map]] <math>p:E \to B</math> is termed a '''weak fibration''' or a '''Serre fibration''' if given any map <math>F:I^n \times I \to B</math> and a map <math>\tilde{f}: I^n \to E</math> such that <math>p(\tilde{f}(x)) = f(x,0)</math>, there exists a map <math>\tilde{F}:I^n \times I \to E</math> satisfying:
 * <math>p \circ \tilde{F} = F</math>
 * <math>F(x,0) = \tilde{f}(x)</math>