Δ-Maximal topologies for some cardinal functions

Abstract

In this paper we introduce the concept of Δ-maximal topologies and characterize Δ-maximal topological spaces for a class of topological properties which include the cardinal functions κ-dense, Sanin, Caliber-κ, and the countable chain condition. In addition special consideration is given to the existence of Δ-maximal κ-dense spaces which are finer than a given κ-dense topology and also investigated are the existence of Δ-maximal second countable spaces.