CW-Complexes and Homotopy

Mahima Ranjan Adhikari ()
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Mahima Ranjan Adhikari: Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)

Chapter Chapter 8 in Basic Algebraic Topology and its Applications, 2016, pp 305-327 from Springer

Abstract: Abstract This chapter conveys a study of a special class of topological spaces, called CW-complexes introduced by J.H.C. Whitehead (1904–1960)Whitehead, J.H.C. (1904–1960) in 1949 with their homotopy properties to meet the need for development of algebraic topology. This class of spaces is broader and has some better categorical properties than simplicial complexes, but still retains a combinatorial nature that allows for computation (often with a much smaller complex). Algebraic topologists now feel that the category of CW-complexes is a good category for homotopy and homology theories.

Keywords: Topological Space; Simplicial Complex; Homotopy Type; Hausdorff Space; Algebraic Topology (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-81-322-2843-1_8

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