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Proceedings of the American Mathematical Society

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

 

 

L'espace des fonctions continues d'un espace métrique dénombrable


Author: Robert Cauty
Journal: Proc. Amer. Math. Soc. 113 (1991), 493-501
MSC: Primary 54C35; Secondary 57N17
MathSciNet review: 1075943
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Abstract: We prove that, for any countable nondiscrete metric space $ X$, the space of continuous real-valued functions on $ X$, with the topology of pointwise convergence, and its subspace of bounded functions, are both homeomorphic to $ {\sigma _\omega }$, the countably infinite product of copies of $ l_f^2$.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1075943-3
Article copyright: © Copyright 1991 American Mathematical Society