Combinatorial Description of Topological Spaces

  • Peter Gabriel
  • Michel Zisman
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE2, volume 35)

Abstract

In this chapter, topological spaces will be denoted by thick capital letters X, Y, Z.... We will write Hom (X, Y) for the simplicial set whose n-th component Jop n × X, Y), and Π 0 (X, Y) will be the set of connected components of Hom (X, Y). The morphisms of complexes
$$^v {\text{X,Y,X}}:\,Hom({\text{X,Y}})\, \times \,Hom({\text{Y,Z}}) \to \,Hom({\text{X,Y}}),$$
,
which are defined “as in V, 7.1”, induce then, by passing to connected components, maps
$$\phi {\text{X,Y,Z}}:\prod _0 ({\text{X,Y}}) \times \prod _0 ({\text{Y,Z}}) \to \prod _0 ({\text{X,Y}}).$$
.

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1967

Authors and Affiliations

  • Peter Gabriel
    • 1
  • Michel Zisman
    • 1
  1. 1.Departement de Mathématique StrasbourgUniversité de StrasbourgFrance

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