Soft Co-Compact Sets

Abstract

In this paper, we introduce and investigate the notion of soft co-compact spaces as a natural generalization of classical co-compact spaces within the framework of soft topology. The aim of this new concept is to provide researchers with a flexible structure through which advanced topological properties-such as generalized compactness, separation axioms, and continuity-can be studied in the context of soft sets. We begin by presenting the formal definition of a soft co-compact space and demonstrating how it extends the classical idea of co-compactness to parameterized environments. Several fundamental properties of this new class are established, and we show that soft co-compact spaces form a distinct category that is not reducible to previously known soft topological constructs. We further explore the interaction between soft co-compactness and various soft separation axioms, thereby revealing new characterizations and criteria that govern their relationships. Motivated by these findings, we introduce associated soft operators-such as soft co-compact interior and soft co-compact closure-and describe their behaviors and structural roles. The developed framework opens a new approach in soft topology, allowing for refined analysis of soft continuity, decomposition theorems, and transitions between different soft topological settings.