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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Small into-isomorphisms between spaces of continuous functions. II


Author: Yoav Benyamini
Journal: Trans. Amer. Math. Soc. 277 (1983), 825-833
MSC: Primary 46E15; Secondary 46B25
MathSciNet review: 694391
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Abstract: We construct two compact Hausdorff spaces, $ X$ and $ Y$, so that $ C(X)$ does not embed isometrically into $ C(Y)$, but for each $ \varepsilon > 0$, there is an isomorphism $ {T_\varepsilon }$ from $ C(X)$ into $ C(Y)$ satisfying $ \parallel f\parallel \leqslant \parallel {T_\varepsilon }f\;\parallel \leqslant (1 + \varepsilon)\parallel f\parallel $ for all $ f \in C(X)$.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0694391-9
Article copyright: © Copyright 1983 American Mathematical Society