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Title

The Vietoris system in strong shape and strong homology

Authors 1

Affiliations

  1. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, Robert-Mayer-Strasse, 6-10 6000 Frankfurt, Germany

Abstract

We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology.

Keywords

ENG
vietoris nerve, Steenrod homotopy category, strong shape theory, strong homology, compact supports

Bibliography

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Additional information

http://matwbn.icm.edu.pl/ksiazki/fm/fm141/fm14124.pdf

Fundamenta Mathematicae
1992/141/2
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Pages:
147-168
Main language of publication
English
Received
1991-08-12
Published
1992
Exact and natural sciences