fibre map

A fibre map is a map of topological spaces $f:E\to B$, for which there exists a space $F$, such that any point of $B$ is contained in some neighbourhood $U$ satisfying the following: on $f^{-1}U$, $f$ restricts to the natural projection $F\times U\to U$, via some homeomorphic identification of $f^{-1}U$ with $F\times U$.

One class of examples are covering maps. Another example is the map $S{O}_3\to S^2$ sending a rotation to the point it sends the “North Pole” to.

Title	fibre map
Canonical name	FibreMap
Date of creation	2013-03-22 14:32:27
Last modified on	2013-03-22 14:32:27
Owner	whm22 (2009)
Last modified by	whm22 (2009)
Numerical id	11
Author	whm22 (2009)
Entry type	Definition
Classification	msc 55R10
Synonym	fiber map
Related topic	FibreBundle
Related topic	LocallyTrivialBundle
Related topic	LongExactSequenceLocallyTrivialBundle
Related topic	Fibration2
Related topic	HomotopyLiftingProperty
Defines	fibre map