The Vietoris system in strong shape and strong homology

Bernd Günther

Fundamenta Mathematicae (1992)

  • Volume: 141, Issue: 2, page 147-168
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Günther, Bernd. "The Vietoris system in strong shape and strong homology." Fundamenta Mathematicae 141.2 (1992): 147-168. <http://eudml.org/doc/211958>.

@article{Günther1992,
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.},
author = {Günther, Bernd},
journal = {Fundamenta Mathematicae},
keywords = {vietoris nerve; Steenrod homotopy category; strong shape theory; strong homology; compact supports; Vietoris system; strong shape; strong ANR-expansion},
language = {eng},
number = {2},
pages = {147-168},
title = {The Vietoris system in strong shape and strong homology},
url = {http://eudml.org/doc/211958},
volume = {141},
year = {1992},
}

TY - JOUR
AU - Günther, Bernd
TI - The Vietoris system in strong shape and strong homology
JO - Fundamenta Mathematicae
PY - 1992
VL - 141
IS - 2
SP - 147
EP - 168
AB - 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.
LA - eng
KW - vietoris nerve; Steenrod homotopy category; strong shape theory; strong homology; compact supports; Vietoris system; strong shape; strong ANR-expansion
UR - http://eudml.org/doc/211958
ER -

References

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