# The Vietoris system in strong shape and strong homology

Fundamenta Mathematicae (1992)

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

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topGünther, 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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