Local triviality of fiberings

Kim, Soon-kyu

doi:10.1090/S0002-9939-1972-0298662-8

Local triviality of fiberings
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Proc. Amer. Math. Soc. 34 (1972), 546-552 Request permission

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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