Selective versions of $\theta$-density

TL;DR

This paper explores selective versions of $ heta$-density in non-regular spaces, linking set-theoretic cardinal numbers with game-theoretic properties of $ heta$-separability.

Contribution

It advances the understanding of $ heta$-separability by connecting it with cardinal invariants and game-theoretic concepts in non-regular spaces.

Findings

Established connections between cardinal numbers and $ heta$-separability

Extended the theory of selective $ heta$-density in non-regular spaces

Linked set-theoretic and game-theoretic perspectives on $ heta$-separability

Abstract

In [8] the authors initiate the study of selective versions of the notion of $\theta$-separability in non-regular spaces. In this paper we continue this investigation by establishing connections between the familiar cardinal numbers arising in the set theory of the real line, and game-theoretic assertions regarding $\theta$-separability.