Closed sets in a generalization of the Alexandrov cube

TL;DR

This paper explores the topology derived from a specific convergence method, focusing on characterizing closed sets and closure operators within complete Boolean algebras that satisfy the countable chain condition.

Contribution

It advances the understanding of the topology associated with the convergence _{ls}, especially in describing closed sets via minimal elements in certain Boolean algebras.

Findings

Characterization of closed sets in the _{ls} topology

Description of closure operators using minimal elements

Application to complete Boolean algebras with countable chain condition

Abstract

We continue work on the topology obtained by the convergence $\lambda_{ls}$, which started in \cite{KuPaCZ}, and further investigated in \cite{KuPaFil19}. The main goal is to describe the closed sets and closure operator by the family of its minimal elements, with the accent on complete Boolean algebras satisfying countable chain condition.