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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
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 $ 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}}{\vert _{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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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

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