Local triviality of fiberings

Kim, Soon-kyu

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

Local triviality of fiberings
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by Soon-kyu Kim

Proc. Amer. Math. Soc. 34 (1972), 546-552

DOI: https://doi.org/10.1090/S0002-9939-1972-0298662-8

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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.

References

On the deformation of an h-cell

9

E. Dyer and M.-E. Hamstrom, Completely regular mappings, Fund. Math. 45 (1958), 103–118. MR 92959, DOI 10.4064/fm-45-1-103-118
Edward Fadell, On fiber spaces, Trans. Amer. Math. Soc. 90 (1959), 1–14. MR 101520, DOI 10.1090/S0002-9947-1959-0101520-0
Mary-Elizabeth Hamstrom, Regular mappings and the space of homeomorphisms on a $3$-manifold, Mem. Amer. Math. Soc. 40 (1961), 42. MR 152999
Mary-Elizabeth Hamstrom and Eldon Dyer, Regular mappings and the space of homeomorphisms on a 2-manifold, Duke Math. J. 25 (1958), 521–531. MR 96202
Soon-kyu Kim, Local triviality of Hurewicz fiber maps, Trans. Amer. Math. Soc. 135 (1969), 51–67. MR 233357, DOI 10.1090/S0002-9947-1969-0233357-2
Soon-kyu Kim, Local triviality of completely regular mappings, Duke Math. J. 38 (1971), 467–471. MR 286132

Replacement and extension theorems in the theory of Hurewicz fiber spaces

L. F. McAuley and P. A. Tulley, Fiber spaces and $n$-regularity, Topology Seminar (Wisconsin, 1965) Ann. of Math. Studies, No. 60, Princeton Univ. Press, Princeton, N.J., 1966, pp. 229–233. MR 0216503
Frank Raymond, Local triviality for Hurewicz fiberings of manifolds, Topology 3 (1965), 43–57. MR 159337, DOI 10.1016/0040-9383(65)90069-8
Frank Raymond, The end point compactification of manifolds, Pacific J. Math. 10 (1960), 947–963. MR 120637

Completely regular mappings

Gerald S. Ungar, Conditions for a mapping to have the slicing structure property, Pacific J. Math. 30 (1969), 549–553. MR 250311
Raymond Louis Wilder, Topology of Manifolds, American Mathematical Society Colloquium Publications, Vol. 32, American Mathematical Society, New York, N. Y., 1949. MR 0029491