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We investigate the relationships among the weaker forms of the properties "Menger", "Alster" and "Lindelöf" in bitopological spaces. We give some counterexamples to show the differences between these properties. Further we introduce the weak versions of the Alster property in terms of selection principles and obtain some of their topological properties.

We study topological games related to weak forms of the Menger property in bitopological spaces. In particular we investigate almost Menger game and its connections to games which are associated with the covering properties consisting of covers containing G δ subsets.