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Proceedings of the American Mathematical Society

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

 

 

A generalization of the Banach-Stone theorem


Author: Bahattin Cengiz
Journal: Proc. Amer. Math. Soc. 40 (1973), 426-430
MSC: Primary 46E15; Secondary 54C99
DOI: https://doi.org/10.1090/S0002-9939-1973-0320723-6
MathSciNet review: 0320723
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Abstract: In this paper the following generalization of the Banach-Stone theorem is proved: If $ \phi $ is a linear isomorphism of an extremely regular linear subspace of $ {C_0}(X)$ onto such a subspace of $ {C_0}(Y)$ with $ \vert\vert\phi \vert\vert\;\vert\vert{\phi ^{ - 1}}\vert\vert < 2$ then $ X$ and $ Y$ are homeomorphic.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320723-6
Article copyright: © Copyright 1973 American Mathematical Society