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|
|Date of creation||2013-03-22 13:15:01|
|Last modified on||2013-03-22 13:15:01|
|Last modified by||mps (409)|