On homeomorphisms of infinite dimensional bundles. II

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

doi:10.1090/s0002-9947-1974-0415626-8

Trans. Amer. Math. Soc.

1974

DOI: 10.1090/s0002-9947-1974-0415626-8

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On homeomorphisms of infinite dimensional bundles. II

T. A. Chapman¹,

R. Y. T. Wong²

Abstract: 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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“…In this paper we extend the results on infinite-dimensional separable .) In a later paper the author and Chapman [19] are able to use results of this paper to extend all the results to bundles modeled on s-manifolds, and in a certain appropriate manner, to bundles modeled on Q-manifolds [20], A main result of this paper is the following characterization of projective Z-sets which then serve as an essential tool to obtain other results. We first need several conventions.…”

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confidence: 99%