locally trivial bundle
A locally trivial bundle is a continuous map of topological spaces such that the following conditions hold. First, each point must have a neighborhood such that the inverse image is homeomorphic to . Second, for some homeomorphism , the diagram
must be commutative (http://planetmath.org/CommutativeDiagram).
Locally trivial bundles are useful because of their covering homotopy property and because each locally trivial bundle has an associated long exact sequence (http://planetmath.org/LongExactSequenceLocallyTrivialBundle) and Serre spectral sequence. Every fibre bundle is an example of a locally trivial bundle.
Title | locally trivial bundle |
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Canonical name | LocallyTrivialBundle |
Date of creation | 2013-03-22 13:15:01 |
Last modified on | 2013-03-22 13:15:01 |
Owner | mps (409) |
Last modified by | mps (409) |
Numerical id | 10 |
Author | mps (409) |
Entry type | Definition |
Classification | msc 55R10 |
Related topic | Fibration |
Related topic | Fibration2 |
Related topic | HomotopyLiftingProperty |