Function spaces and local characters of topological spaces

Tereda, Toshiji

doi:10.1090/S0002-9939-1988-0915744-7

Function spaces and local characters of topological spaces
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Proc. Amer. Math. Soc. 102 (1988), 202-204 Request permission

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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The coincidence of the dimension dim of

-equivalent topological spaces

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