Singular Vietoris-Begle theorems for relations

Bourgin, D. G.; Nehs, Robert M.

doi:10.1090/S0002-9947-1984-0742426-8

Singular Vietoris-Begle theorems for relations
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by D. G. Bourgin and Robert M. Nehs PDF

Trans. Amer. Math. Soc. 284 (1984), 281-318 Request permission

Abstract:

The Vietoris-Begle theorem with singularities, for three spaces $X$, $Y$, $T$, is extended to the case that a closed relation replaces a continuous map and more generally to set valued maps. The developments are carried out based on modification of the topology of $T$ so that in general it is no longer even Hausdorff. This entails interpretation of dimension of singulars sets in terms of considertions in $Y$ rather than $T$. The techniques are those of sheaf and spectral sequence theory.

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