τ-closed and τ-open sets and their properties: τ-closed and τ-open sets and their properties

Abstract

The article presents the properties of the τ-closure operator and their proofs. Also,
these properties help to better understand the definitions and examples of τ-closed sets, τ-open sets, τneighborhood, τ-interior, and τ-boundary of sets. As an innovation presented in the article, the theorem
relating the τ-closure operator of a set to the Cartesian product of sets and its proof are presented in
detail, and the conclusions arising from it are given.