On homeomorphisms of infinite dimensional bundles. II

Chapman, T. A.; Wong, R. Y. T.

doi:10.1090/S0002-9947-1974-0415626-8

On homeomorphisms of infinite dimensional bundles. II
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by T. A. Chapman and R. Y. T. Wong PDF

Trans. Amer. Math. Soc. 191 (1974), 261-268 Request permission

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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