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Selection principles and games in bitopological function spaces

Lyakhovets Daniil (Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia)
Osipov Alexander V. (Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ural State University of Economics, Yekaterinburg, Russia)

For a Tychonoff space X, we denote by (C(X), τk τp) the bitopological space of all real-valued continuous functions on X, where τk is the compact-open topology and τp is the topology of pointwise convergence. In the papers [6, 7, 13] variations of selective separability and tightness in (C(X),τk,τp) were investigated. In this paper we continue to study the selective properties and the corresponding topological games in the space (C(X),τk,τp).

Keywords: Selection principles, compact-open topology, function space, bitopological space, topological games, separable space