Interior and closure in anti-minimal and anti-biminimal spaces in the frame of anti-topology

Abstract

The main goal of this project is to analyze the structure of anti-biminimal spaces through the
lens of the notions of interior and closure. Anti-biminimal spaces can be considered as generalizations of antibitopological spaces that have been introduced and studied earlier. On the other hand, they can be viewed as
counterparts of biminimal spaces. Finally, they are spaces equipped with two anti-minimal structures. Thus,
we show some basic results on the latter. In particular, we refer to the concepts of density, nowhere density
and rarity in anti-minimal spaces.
In general, anti-topology is a structure κ in which at least one classical axiom is totally false. In this paper,
we consider the first axiom. Hence, ∅ and X do not belong to κ.