Cellular homotopy theorem: Difference between revisions
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{{homotopy theorem}} | |||
==Statement== | ==Statement== | ||
Suppose <math>(X,A)</math> and <math>(Y,B)</math> are [[relative CW-complex]]es (i.e. CW-pairs). Let <math>f:(X,A) \to (Y,B)</math> be a continuous map. Then there exists a [[cellular map]] <math>g:(X,A) \to (Y,B)</math> such that <math>f</math> and <math>g</math> are homotopic relative to <math>A</math> (that is, the homotopy does not change the restriction of the function to <math>A</math> at all). | Suppose <math>(X,A)</math> and <math>(Y,B)</math> are [[relative CW-complex]]es (i.e. CW-pairs). Let <math>f:(X,A) \to (Y,B)</math> be a continuous map. Then there exists a [[cellular map]] <math>g:(X,A) \to (Y,B)</math> such that <math>f</math> and <math>g</math> are homotopic relative to <math>A</math> (that is, the homotopy does not change the restriction of the function to <math>A</math> at all). | ||
Revision as of 00:25, 27 October 2007
Statement
Suppose and are relative CW-complexes (i.e. CW-pairs). Let be a continuous map. Then there exists a cellular map such that and are homotopic relative to (that is, the homotopy does not change the restriction of the function to at all).
