fibre map

A fibre map is a map of topological spacesMathworldPlanetmath f:EB, for which there exists a space F, such that any point of B is contained in some neighbourhood U satisfying the following: on f-1U, f restricts to the natural projection F×UU, via some homeomorphic identification of f-1U with F×U.

One class of examples are covering maps. Another example is the map SO3S2 sending a rotation to the point it sends the “North PoleMathworldPlanetmath” 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