Weaker forms of the Menger property in bitopological spaces

Games relating to weak covering properties in bitopological spaces

“…In [14] Kočinac introduced the notion of almost Menger property in topological spaces and in [9,10,18] this notion was investigated in the bitopological context. Now in this section we consider the almost Menger game on bitopological spaces and relate this notion to (i, j) -almost Menger property.…”

“…On the other hand, there are quite a few studies on the weak versions of covering properties in bitopological spaces. They are mainly related to weak versions of the Menger property such as almost Menger, weakly Menger and their connections with the Menger property in bitopological spaces (see, [9,10,18]). However there is no systematic study of weak covering properties and their relations with game theory in bitopological context.…”

Investigations onweak versions of the Alster property in bitopological spaces and selection principles

“…We end this section by recalling from [10,25] the definitions of almost Menger and weakly Menger properties in bitopological spaces. Our topological terminology and notations are as in the book [9] and standard reference for bitopological spaces is [7].…”

“…From the definitions, it is clear that every (i, j)-almost Menger bitopological space is (i, j)-weakly Menger but the converse does not hold (see, Exp.2.3 in [10]).…”

“…The weak versions of the Lindelöf property in bitopological spaces were mostly studied in [15]. Selective versions of the Lindelöf property for example Menger and Rothberger properties and their weaker forms as almost Menger and weakly Menger properties in bitopological spaces were discussed in [10,25].…”