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

DOI:
https://doi.org/10.1090/S0002-9939-1970-0266163-7

MathSciNet review:
0266163

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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 $Q$.

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Keywords:
Fréchet space,
Hilbert cube,
compactification,
homeomorphism,
extending homeomorphism,
property Z

Article copyright:
© Copyright 1970
American Mathematical Society