Menger type properties in bitopology: Equivalences and games

Abstract

This paper contributes to the recent researches on weaker forms
of the Menger property in bitopological spaces. It carries
on the investigation deeper in this area, examining various
equivalent conditions and present game -theoretic observations
related to weaker forms of the Menger-type properties.
Furthermore we define a new type of Menger property,
nearly Mengerness and discuss its properties with in the
context of bitopological spaces.