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: In the study of extending homeomorphisms in the compactification of Fréchet spaces into the Hilbert cube , it is shown that for a given homeomorphism of onto itself and a closed subset of satisfying property in , there is a homeomorphism of onto itself such that extends to a homeomorphism of onto . The proof is by employing the rather useful shifting homeomorphism on .

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Additional Information

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

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

Article copyright:
© Copyright 1970
American Mathematical Society