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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Singular Vietoris-Begle theorems for relations


Authors: D. G. Bourgin and Robert M. Nehs
Journal: Trans. Amer. Math. Soc. 284 (1984), 281-318
MSC: Primary 55N30; Secondary 54A10, 54C60, 55T25
MathSciNet review: 742426
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0742426-8
PII: S 0002-9947(1984)0742426-8
Keywords: Vietoris-Begle theorem, sheaf, spectral sequence, paracompact, graph, identification topology
Article copyright: © Copyright 1984 American Mathematical Society