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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cones and Vietoris-Begle type theorems


Author: D. G. Bourgin
Journal: Trans. Amer. Math. Soc. 174 (1972), 155-183
MSC: Primary 55B30
MathSciNet review: 0322854
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Abstract: Infinite cone constructions are exploited to yield diverse generalizations of the Vietoris-Begle theorem for paracompact spaces and Abelian group sheaves. The constructions suggest natural space, map classifications designated as almost p-solid. The methods are extended to upper semicontinuous closed multivalued maps and homotopies and culminate in a disk fixed point theorem for possibly nonacyclic point images.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0322854-7
Keywords: Vietoris-Begle theorem, sheaf, paracompact, quotient space, Tychonoff parallelotope, exact sequence, support family, upper semicontinuity, graph
Article copyright: © Copyright 1972 American Mathematical Society