Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Extending homeomorphisms in compactification of Fréchet spaces

Author: Raymond Y. T. Wong
Journal: Proc. Amer. Math. Soc. 25 (1970), 548-550
MSC: Primary 54.53
MathSciNet review: 0266163
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In the study of extending homeomorphisms in the compactification of Fréchet spaces into the Hilbert cube $Q$, it is shown that for a given homeomorphism $f$ of $s$ onto itself and a closed subset $K$ of $s$ satisfying property $Z$ in $s$, there is a homeomorphism $g$ of $s$ onto itself such that $gf{g^{ - 1}}{|_{g(K)}}$ extends to a homeomorphism of $Q$ onto $Q$. The proof is by employing the rather useful shifting homeomorphism on $Q$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.53

Retrieve articles in all journals with MSC: 54.53

Additional Information

Keywords: Fréchet space, Hilbert cube, compactification, homeomorphism, extending homeomorphism, property Z
Article copyright: © Copyright 1970 American Mathematical Society