Homotopy Type of CW Complexes

  • Albert T. Lundell
  • Stephen Weingram
Part of the The University Series in Higher Mathematics book series (USHM)


In this chapter we will study conditions on a space that will cause it to have the homotopy type of a CW complex and prove a theorem of J. H. C. Whitehead which gives a criterion that a map between two such spaces be a homotopy equivalence. We note in passing that there is a method using elaborate algebraic techniques (the analysis of Postnikov systems) for determining, in principle, whether two such spaces have the same homotopy type, but this is beyond the scope of this book.


Simplicial Complex Homotopy Type Homotopy Group Mapping Cylinder Deformation Retract 
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Copyright information

© Litton Educational Publishing, Inc. 1969

Authors and Affiliations

  • Albert T. Lundell
    • 1
  • Stephen Weingram
    • 2
  1. 1.University of ColoradoBoulderUSA
  2. 2.Purdue UniversityLafayetteUSA

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