# fibre map

A fibre map is a map of topological spaces $f:E\rightarrow B$, 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 $F\times U\rightarrow U$, via some homeomorphic identification of $f^{-1}U$ with $F\times U$.

One class of examples are covering maps. Another example is the map $SO_{3}\rightarrow S^{2}$ 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