Set-theoretic topology and some properties of the closure operation of a collection of sets

In this paper, we develops an approach to the presentation of set-theoretic topology based on the systematic use of two standard operations: the union operation and the closure operation of a collection of sets (i.e., the closure with respect to the union operation). Definitions of these operations are given and their basic properties are formulated and proved. Based on the results obtained, the foundations of elementary topology are constructed.