Geodesic
The Vietoris system in strong shape and strong homology
Fundamenta Mathematicae, Tome 141 (1992) no. 2, pp. 147-168

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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.
DOI : 10.4064/fm-141-2-147-168
Keywords: vietoris nerve, Steenrod homotopy category, strong shape theory, strong homology, compact supports 
Bernd Günther. The Vietoris system in strong shape and strong homology. Fundamenta Mathematicae, Tome 141 (1992) no. 2, pp. 147-168. doi: 10.4064/fm-141-2-147-168
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