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Spaces of continuous functions, box products and almost- $ω$ -resolvable spaces

Angel Tamariz-Mascarúa; H. Villegas-Rodríguez — 2002

Commentationes Mathematicae Universitatis Carolinae

A dense-in-itself space $X$ is called if the space of real continuous functions on $X$ with its box topology, $C_{□} (X)$ , is a discrete space. A space $X$ is called provided that $X$ is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with $κ$ -resolvable and almost resolvable spaces. We prove that every almost- $ω$ -resolvable space is $C_{□}$ -discrete, and that these classes coincide in the realm of completely regular...

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