On spaces of group-valued functions
The author extends several results concerning closure-type properties of continuous real-valued functions on a Tychonoff space, to the space \(C_p(X,G)\) of group-valued functions with the topology of pointwise convergence, investigated by \textit{D. Shakhmatov} and \textit{J. Spévák} [Topology Appl. 157, 1518--1540 (2010; Zbl 1195.54040)]. For example, it is proved that \(X\) satisfies the selection principle \(S_1(\Omega,\Omega)\) if and only if \(C_p(X,G)\) has countable strong fan tightness, where \(G\) is a metric group and \(X\) is a \(G^*\)-regular space.NEWLINENEWLINE In the third section, some results from the previous section and from [\textit{A. Caserta, G. Di Maio} and \textit{Lj. D. R. Kočinac}, Topology Appl. 159, 1847--1852 (2012; Zbl 1253.54021)] are extended to the function space \(C(X,G)\) endowed with the topology of strong uniform convergence on bornologies.
scientific article; zbMATH DE number 6217182