K‐Structures and Topology

Abstract

ABSTRACT: K‐structures allow one to give purely set‐theoretic proofs of a number of important inequalities in cardinal functions. We explore the precise relationship between K‐structures, closure spaces in the sense of Čech, spaces with the weak topology in the sense of Arhangelskiǐ, and topological spaces. We also introduce the notion of a basic proximity space and establish the connection between K‐structures and basic proximity spaces.