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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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 $Q$.

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