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 -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