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.

**[1]**J. W. Alexander,*On the deformation of an h-cell*, Proc. Nat. Acad. Sci. U.S.A.**9**(1923), 406-407.**[2]**E. Dyer and M.-E. Hamstrom,*Completely regular mappings*, Fund. Math.**45**(1958), 103-118. MR**19**, 1187. MR**0092959 (19:1187e)****[3]**E. Fadell,*On fiber spaces*, Trans. Amer. Math. Soc.**90**(1959), 1-14. MR**21**#330. MR**0101520 (21:330)****[4]**M.-E. Hamstrom,*Regular mappings and the space of homeomorphisms on a 3-manifold*, Mem. Amer. Math. Soc. No. 40 (1961). MR**27**#2970. MR**0152999 (27:2970)****[5]**M.-E. Hamstrom and E. Dyer,*Regular mappings and the space of homeomorphisms on a 2-manifold*, Duke Math. J.**25**(1958), 521-531. MR**20**#2695. MR**0096202 (20:2695)****[6]**S. K. Kim,*Local triviality of Hurewicz fiber maps*, Trans. Amer. Math. Soc.**135**(1969), 51-67. MR**38**#1679. MR**0233357 (38:1679)****[7]**-,*Local triviality of completely regular mappings*, Duke Math. J.**38**(1971), 467-471. MR**0286132 (44:3346)****[8]**S. L. Langston,*Replacement and extension theorems in the theory of Hurewicz fiber spaces*, Thesis, University of Wisconsin, Madison, Wis., 1968.**[9]**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**35**#7336. MR**0216503 (35:7336)****[10]**F. Raymond,*Local triviality for Hurewicz fiberings of manifolds*, Topology**3**(1965), 43-57. MR**0159337 (28:2554)****[11]**-,*The end point compactification of manifolds*, Pacific J. Math.**10**(1960), 947-963. MR**22**#11387. MR**0120637 (22:11387)****[12]**S. B. Seidman,*Completely regular mappings*, Thesis, University of Michigan, Ann Arbor, Mich., 1969.**[13]**G. S. Ungar,*Conditions for a mapping to have the slicing structure property*, Pacific J. Math.**30**(1969), 549-553. MR**40**#3550. MR**0250311 (40:3550)****[14]**R. L. Wilder,*Topology of manifolds*, Amer. Math. Soc. Colloq. Publ., vol. 32, Amer. Math. Soc., Providence, R.I., 1949. MR**10**, 614. MR**0029491 (10:614c)**

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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