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Extending homeomorphisms and applications to metric linear spaces without completeness


Author: Tadeusz Dobrowolski
Journal: Trans. Amer. Math. Soc. 313 (1989), 753-784
MSC: Primary 57N17; Secondary 54C20, 58B10
DOI: https://doi.org/10.1090/S0002-9947-1989-0930078-8
MathSciNet review: 930078
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Abstract: A method of extending homeomorphisms between compacta metric spaces is presented. The main application is that homeomorphisms between compacta of an infinite-dimensional locally convex metric linear space extend to the whole space. A lemma used in the proof of this fact together with the method of absorbing sets is employed to show that every $ \sigma $ -compact normed linear space is homeomorphic to a dense linear subspace of a Hilbert space. A discussion of the relative topological equivalence of absorbing sets in noncomplete spaces is included. The paper is concluded with some controlled versions of an isotopy extension theorem.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1989-0930078-8
Keywords: Homeomorphism extension property, almost extension property, locally convex linear space, skeleton sets
Article copyright: © Copyright 1989 American Mathematical Society

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