On homeomorphisms of infinite dimensional bundles. II

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

Journal:
Trans. Amer. Math. Soc. **191** (1974), 261-268

MSC:
Primary 57A20; Secondary 58B05

MathSciNet review:
0415626

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Abstract: This paper presents some aspects of homeomorphism theory in the setting of (fibre) bundles modeled on separable Hilbert manifolds and generalizes results previously established. The main result gives a characterization of subsets of infinite deficiency in a bundle by means of their restriction to the fibres, from which we are able to prove theorems of the following types: (a) mapping replacement, (b) separation of sets, (c) negligibility of subsets, and (d) extending homeomorphisms.

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DOI:
https://doi.org/10.1090/S0002-9947-1974-0415626-8

Keywords:
Bundle,
polyhedron,
homeomorphism,
ambient isotopy

Article copyright:
© Copyright 1974
American Mathematical Society