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- W1493669845 abstract "Let $X$ be a zero-dimensional metric space and $X'$ its derived set. We prove the following assertions: (1) the space $C_k(X,2)$ is an Ascoli space iff $C_k(X,2)$ is $k_mathbb{R}$-space iff either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (2) $C_k(X,2)$ is a $k$-space iff either $X$ is a topological sum of a Polish locally compact space and a discrete space or $X$ is not locally compact but $X'$ is compact, (3) $C_k(X,2)$ is a sequential space iff $X$ is a Polish space and either $X$ is locally compact or $X$ is not locally compact but $X'$ is compact, (4) $C_k(X,2)$ is a Fr'{e}chet--Urysohn space iff $C_k(X,2)$ is a Polish space iff $X$ is a Polish locally compact space, (5) $C_k(X,2)$ is normal iff $X'$ is separable, (6) $C_k(X,2)$ has countable tightness iff $X$ is separable. In cases (1)-(3) we obtain also a topological and algebraical structure of $C_k(X,2)$." @default.
- W1493669845 created "2016-06-24" @default.
- W1493669845 creator A5023391268 @default.
- W1493669845 date "2015-04-16" @default.
- W1493669845 modified "2023-09-26" @default.
- W1493669845 title "Topological properties of function spaces $C_k(X,2)$ over zero-dimensional metric spaces $X$" @default.
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- W1493669845 doi "https://doi.org/10.48550/arxiv.1504.04198" @default.
- W1493669845 hasPublicationYear "2015" @default.
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