Study on Anti Topological Ordered Spaces

Abstract

In the exploration of topological spaces across various contexts, the cornerstone concepts revolve around open sets, closed sets, as well as the notions of interior and exterior of a set. Equivalently fundamental are the foundational principles encountered when delving into the realm of Anti-topological spaces (ATS). The landscape of mathematical inquiry delves into the intricate definitions and properties of anti-open sets, anti-closed sets, anti-interiors, anti-exteriors, as well as b-anti-open sets, b-anti-closed sets, anti-b-interiors, and anti-b-closures, among a rich array of others. Scholars worldwide have not only encountered but also delved deep into these foundational ideas. This article introduces, studies, and analyzes fundamental properties of concepts like Anti-g-closed, Anti-g-open, Anti-ig-closed, Anti-dg-closed, and Anti-bg-closed specifically within the context of “Anti-topological ordered spaces (ATOS)”.