Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


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
MathSciNet review: 930078
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57N17, 54C20, 58B10

Retrieve articles in all journals with MSC: 57N17, 54C20, 58B10

Additional Information

PII: S 0002-9947(1989)0930078-8
Keywords: Homeomorphism extension property, almost extension property, locally convex linear space, skeleton sets
Article copyright: © Copyright 1989 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia