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On homeomorphisms of infinite-dimensional bundles. I


Author: Raymond Y. T. Wong
Journal: Trans. Amer. Math. Soc. 191 (1974), 245-259
MSC: Primary 57A20; Secondary 58B05
DOI: https://doi.org/10.1090/S0002-9947-1974-0415625-6
MathSciNet review: 0415625
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Abstract: In this paper we present several aspects of homeomorphism theory in the setting of fibre bundles modeled on separable infinite-dimensional Hilbert (Fréchet) spaces. We study (homotopic) negligibility of subsets, separation of sets, characterization of subsets of infinite-deficiency and extending homeomorphisms; in an essential way they generalize previously known results for manifolds. An important tool is a lemma concerning the lifting of a map to the total space of a bundle whose image misses a certain closed subset presented as obstruction; from this we are able to obtain a result characterizing all subsets of infinite deficiency (for bundles) by their restriction to each fibre. Other results then follow more or less routinely by employing the rather standard methods of infinite-dimensional topology.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0415625-6
Keywords: Bundle, polyhedron, homeomorphism, ambient isotopy, deletion, separation, extension
Article copyright: © Copyright 1974 American Mathematical Society

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