Fibration: Difference between revisions
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{{ | {{continuous map property}} | ||
==Definition== | ==Definition== | ||
A continuous map <math>p:E \to B</math> of [[topological space]]s is termed a '''fibration''' or is said to have the '''homotopy lifting property''' if, given any map <math>F:X \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}:X \times I \to E</math> satisfying: | A [[continuous map]] <math>p:E \to B</math> of [[topological space]]s is termed a '''fibration''' or is said to have the '''homotopy lifting property''' if it is ''surjective'' and, given any map <math>F:X \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}:X \times I \to E</math> satisfying: | ||
* <math>p \circ \tilde{F} = F</math> | * <math>p \circ \tilde{F} = F</math> | ||
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This is dual to the notion of a [[cofibration]]. | This is dual to the notion of a [[cofibration]]. | ||
==Relation with other properties== | |||
===Weaker properties=== | |||
* [[Weak fibration]] (also called Serre fibration) | |||
Latest revision as of 00:45, 25 December 2010
This article defines a property of continuous maps between topological spaces
Definition
A continuous map of topological spaces is termed a fibration or is said to have the homotopy lifting property if it is surjective and, given any map and a map such that , there exists a map satisfying:
This is dual to the notion of a cofibration.
Relation with other properties
Weaker properties
- Weak fibration (also called Serre fibration)