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.
@article{bwmeta1.element.bwnjournal-article-fmv141i2p147bwm,
author = {Bernd G\"unther},
title = {The Vietoris system in strong shape and strong homology},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {147-168},
zbl = {0772.55007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv141i2p147bwm}
}
Günther, Bernd. The Vietoris system in strong shape and strong homology. Fundamenta Mathematicae, Tome 141 (1992) pp. 147-168. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv141i2p147bwm/
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