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Transactions of the American Mathematical Society

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

 

 

Function spaces of completely metrizable spaces


Authors: Jan Baars, Joost de Groot and Jan Pelant
Journal: Trans. Amer. Math. Soc. 340 (1993), 871-883
MSC: Primary 54C35; Secondary 57N17
DOI: https://doi.org/10.1090/S0002-9947-1993-1160154-X
MathSciNet review: 1160154
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Abstract: Let $ X$ and $ Y$ be metric spaces and let $ \phi :{C_p}(X) \to {C_p}(Y)$ (resp. $ \phi :C_p^\ast(X) \to C_p^\ast(Y)$) be a continuous linear surjection. We prove that $ Y$ is completely metrizable whenever $ X$ is. As a corollary we obtain that complete metrizability is preserved by $ {l_p}$ (resp. $ l_p^\ast$-equivalence) in the class of all metric spaces. This solves Problem 35 in [2] (raised by Arhangel'skiĭ).


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DOI: https://doi.org/10.1090/S0002-9947-1993-1160154-X
Keywords: Function spaces, completely metrizable spaces
Article copyright: © Copyright 1993 American Mathematical Society