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Proceedings of the American Mathematical Society

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

 

 

Function spaces and local characters of topological spaces


Author: Toshiji Tereda
Journal: Proc. Amer. Math. Soc. 102 (1988), 202-204
MSC: Primary 54C30,; Secondary 46E10
MathSciNet review: 915744
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Abstract: We write $ V \simeq W$ to mean that the two linear topological spaces $ V$ and $ W$ are linearly homeomorphic. In this paper we prove: (1) There are compact spaces $ X,Y$ for which $ {C_p}\left( X \right) \simeq {C_p}\left( Y \right)$ and $ \chi \left( X \right) \ne \chi \left( Y \right)$ are satisfied. (2) For each infinite cardinal $ \kappa $, there are spaces $ X,Y$ for which $ {C_p}\left( X \right) \simeq {C_p}\left( Y \right),\chi \left( X \right) = \omega $ and $ \psi \left( Y \right) = \kappa $. (3) For each infinite cardinal $ \kappa $, there are spaces $ X,Y$ for which $ {C_p}\left( X \right) \simeq {C_p}\left( Y \right),\pi \chi \left( X \right) = \omega $ and $ \pi \chi \left( Y \right) = \kappa $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0915744-7
Keywords: Real-valued continuous function, linear homeomorphism, character, pseudocharacter, $ \pi $-character
Article copyright: © Copyright 1988 American Mathematical Society