On some Separation Axioms in Soft Lattice Topological Spaces

Abstract

In the realm of topology, various constraints are frequently imposed on the types of topological spaces under examination and these constraints are defined by what are known as separation axioms. Also, the separation axioms can be seen as additional conditions that may be incorporated into the definition of topological spaces. Separation axioms serve various purposes in lattice theory. They provide tools for classifying and comparing different lattices, revealing their structural and topological properties. While traditional separation axioms like T₀, T₁, T₂, etc., still play a role, their interpretation and implications differ in the context of soft sets and lattice structures. This paper introduces the separation axioms, soft lattice -space (for i = 4, 5, 6), within the context of a soft lattice topological space and investigates several of their associated properties. Studying lattices through these axioms can reveal connections between their order-theoretic properties and their topological features. This work goes beyond simply applying separation axioms to soft lattice topological spaces. It ventures into unveiling soft lattice invariant properties. Additionally, the study explores soft lattice invariant properties that are derived from these soft lattice -space concepts, specifically, soft lattice hereditary and soft lattice topological properties. In conclusion, the study's exploration of soft lattice invariant properties pushes the boundaries of understanding soft lattice topological spaces. By delving into the essence of these structures and their local and global characteristics, the study opens doors to exciting theoretical possibilities and potential applications in diverse fields.

Received 16/10/2023

Revised 01/03/2024

Accepted 03/03/2024

Published Online First 20/05/2024