Exploring critical cardinalities via selection principles and games

Abstract

The study of cardinal characteristics \(\mathfrak {b}\) and \(\mathfrak {d}\) is well known in set-theoretic and general topology. In this paper, we present characterizations of \(\mathfrak {b}\) and \(\mathfrak {d}\) using selective properties, sub-bounded and sub-dominating families. In addition, we define infinitely long two-player games to present other characterizations of the critical cardinalities \(\mathfrak {b}\) and \(\mathfrak {d}\).