A note on a novel type of Alster covering property in bitopological setting

In this paper, we introduce a new type of Alster covering property in bitopological setting. We investigate its relations with other existing covering properties. By giving counterexamples, we indicate that our new property is different than other mentioned properties. We also construct some conditions for equivalences of those properties with the corresponding property. We also consider the preservation of this new form of bitopological Alster covering property. We investigate the productivity of bitopological nearly Lindelöfness and bitopological nearly Mengerness.