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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Local triviality of fiberings


Author: Soon-kyu Kim
Journal: Proc. Amer. Math. Soc. 34 (1972), 546-552
MSC: Primary 55F05
DOI: https://doi.org/10.1090/S0002-9939-1972-0298662-8
MathSciNet review: 0298662
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Abstract: We prove that a Hurewicz fibering or a Serre fibering is locally trivial if the total space is a connected separable metric ANR n-gm over a principal ideal domain and the base space is a weakly locally contractible paracompact finite dimensional space, and all fibers are homeomorphic to a space which is a connected 3-manifold with exactly one end and whose one point compactification is a 3-manifold and it has no false 3-cells, in particular a euclidean 3-space.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0298662-8
Keywords: Hurewicz fiber map, Serre fiber map, homotopically n-regular map, locally trivial map, n-gm, wlc, ends, one-point compactification
Article copyright: © Copyright 1972 American Mathematical Society