On homeomorphisms of infinite dimensional bundles. III

Authors:
T. A. Chapman and R. Y. T. Wong

Journal:
Trans. Amer. Math. Soc. **191** (1974), 269-276

MSC:
Primary 57A20; Secondary 58B05

MathSciNet review:
0415627

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we continue the study of homeomorphisms and prove an analogue of the homeomorphism extension theorem for bundles modeled on Hilbert cube manifolds; thus we generalize previous results for *Q*-manifolds (Anderson-Chapman). This analogy, as in the case of manifolds, requires a consideration of proper maps and proper homotopies. The approach to the present problem is similar to that considered in our previous papers. Bear in mind several distinct difficulties occur in our setting.

**[1]**R. D. Anderson,*Topological properties of the Hilbert cube and the infinite product of open intervals*, Trans. Amer. Math. Soc.**126**(1967), 200–216. MR**0205212**, 10.1090/S0002-9947-1967-0205212-3**[2]**R. D. Anderson,*On topological infinite deficiency*, Michigan Math. J.**14**(1967), 365–383. MR**0214041****[3]**R. D. Anderson and T. A. Chapman,*Extending homeomorphisms to Hilbert cube manifolds*, Pacific J. Math.**38**(1971), 281–293. MR**0319204****[4]**R. D. Anderson, David W. Henderson, and James E. West,*Negligible subsets of infinite-dimensional manifolds*, Compositio Math.**21**(1969), 143–150. MR**0246326****[5]**R. D. Anderson and John D. McCharen,*On extending homeomorphisms to Fréchet manifolds*, Proc. Amer. Math. Soc.**25**(1970), 283–289. MR**0258064**, 10.1090/S0002-9939-1970-0258064-5**[6]**T. A. Chapman,*Dense sigma-compact subsets of infinite-dimensional manifolds*, Trans. Amer. Math. Soc.**154**(1971), 399–426. MR**0283828**, 10.1090/S0002-9947-1971-0283828-7**[7]**Raymond Y. T. Wong,*On homeomorphisms of infinite-dimensional bundles. I*, Trans. Amer. Math. Soc.**191**(1974), 245–259. MR**0415625**, 10.1090/S0002-9947-1974-0415625-6**[8]**T. A. Chapman and R. Y. T. Wong,*On homeomorphisms of infinite dimensional bundles. II*, Trans. Amer. Math. Soc.**191**(1974), 261–268; ibid. 191 (1974), 269–276. MR**0415626**, 10.1090/S0002-9947-1974-0415626-8

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0415627-X

Keywords:
Hilbert cube manifolds,
bundles,
*B*-preserving homeomorphism,
extension,
mapping replacement,
separation

Article copyright:
© Copyright 1974
American Mathematical Society