Soft optimal functions and soft semi-hausdorff spaces

This paper presents and investigates the concept of soft optimal maps within the framework of soft topological spaces. A soft map is called soft optimal if it preserves soft disjointness for soft open sets in the soft structure. The link between soft injectivity and soft optimality is investigated, revealing that every soft injective map is soft optimal, but the converse is not true. Some correlations between this class of soft optimal maps and its analogs in general topology are given. The paper further shows that soft optimality is independent of all forms of soft continuity, soft openness, and soft closedness. Furthermore, the impact of soft optimality on soft semi-Hausdorff and soft Hausdorff properties is considered with concrete theorems showing how soft optimality affects the soft semi-Hausdorff state in soft topological spaces under various soft continuity assumptions. Finally, we show that the soft optimal map, which is soft s-open and soft pre-continuous, will preserve soft disjointness for the class of soft semi-open sets.

کلیدواژه ها:

Soft Hausdorff ، soft semi-Hausdorff ، soft pre-continuous function ، soft semi-continuous function ، generated soft topology