Pansera, B. A.; Pavlović, V. Open covers and function spaces. (English) Zbl 1119.54013 Mat. Vesn. 58, No. 1-2, 57-70 (2006). An open cover \(\mathcal U\) of a space \(X\) is said to be an \(\omega\)-cover (a \(k\)-cover) if \(X\notin\mathcal U\) and each finite (compact) subset of \(X\) is contained in a member of \(\mathcal U\). For a space \(X\), \(S_1(\mathcal K,\Omega)\) denotes the property that for each sequence \((\mathcal U_n)_{n<\infty}\) of \(k\)-covers of \(X\) there are \(U_n\in\mathcal U_n\), \(n<\infty\), such that \(\{U_n:n<\infty\}\) is an \(\omega\)-cover of \(X\). This property is characterized by a closure property of the set \(C(X)\) of continuous real-valued functions on \(X\) equipped with the compact-open and pointwise topologies. For the set \(C(X)\) with the same two topologies, the authors characterize the selective bitopological versions of the Reznichenko and Pytkeev properties, introduced by the reviewer [Acta Math. Hungar. 107, 225–233 (2005; Zbl 1082.54007)] in the context of hyperspaces. Reviewer: Ljubiša Kočinac (Niš) Cited in 8 Documents MSC: 54C35 Function spaces in general topology 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) Keywords:\(\omega\)-cover; \(k\)-cover; selection principles; pointwise topology; compact-open topology; Reznichenko property; Pytkeev property Citations:Zbl 1082.54007 PDFBibTeX XMLCite \textit{B. A. Pansera} and \textit{V. Pavlović}, Mat. Vesn. 58, No. 1--2, 57--70 (2006; Zbl 1119.54013) Full Text: EuDML