In this paper, we give a characterization for $C_k(X)$ to satisfy $S_{fin}(\mathcal{S},\mathcal{S})$.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on $X$ with the compact-open topology.
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Temel Bulgular & Veri:A subset $A\subset X$ is said to be sequentially dense in $X$ if every point of $X$ is the limit of a convergent sequence in $A$.
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Sonuç & Katkı:In this paper, we give a characterization for $C_k(X)$ to satisfy $S_{fin}(\mathcal{S},\mathcal{S})$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:compact-open topology · function space · selectively sequentially separable
Abstract
For a Tychonoff space $X$, we denote by $C_k(X)$ the space of all real-valued continuous functions on $X$ with the compact-open topology. A subset $A\subset X$ is said to be sequentially dense in $X$ if every point of $X$ is the limit of a convergent sequence in $A$. A space $C_k(X)$ is selectively sequentially separable (in Scheepers' terminology: $C_k(X)$ satisfies $S_{fin}(\mathcal{S},\mathcal{S})$) if whenever $(S_n : n\in \mathbb{N})$ is a sequence of sequentially dense subsets of $C_k(X)$, one can pick finite $F_n\subset S_n$ ($n\in \mathbb{N}$) such that $\bigcup \{F_n: n\in \mathbb{N}\}$ is sequentially dense in $C_k(X)$. In this paper, we give a characterization for $C_k(X)$ to satisfy $S_{fin}(\mathcal{S},\mathcal{S})$.
Osipov, A. V. (2022). On selective sequential separability of function spaces with the compact-open topology. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 6, 1761–1766. https://ajindex.com/articles/530114
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