On Soft P Beta Alpha Open Set in Soft Topological Space

Jamil, Ansam

doi:10.25673/123714

Proceedings of International Conference on Applied Innovation in IT · 2026/03/31 · Vol. 14 · Issue 1 · pp. 1183–1188

On Soft P Beta Alpha Open Set in Soft Topological Space

Ansam Hussein Ekal and Jamil Mahmoud Jamil

📄 Download PDF DOI: 10.25673/123714

Abstract

In this work, a new class of soft open sets, called soft pβα-open sets, is introduced and several fundamental properties and characterizations of this concept are established. The relationships between soft pβα-open sets and other well-known classes of soft open sets are also investigated. In addition, the notion of soft pβα-closed sets is introduced and studied through various classifications and properties. The paper also reviews several basic concepts in soft set theory and soft topological spaces that are required for the development of the proposed results. Definitions and operations related to soft sets, including union, intersection, closure, and interior operators, are considered within the framework of soft topology. Furthermore, the role of dense soft sets and their associated topological properties is examined. The obtained results provide a broader understanding of generalized soft open and closed sets and clarify their relationships with existing concepts in soft topology. It is expected that these findings may contribute to further developments and applications of soft topological structures in mathematical analysis, uncertainty modeling, and decision-making problems.

Keywords

Soft α-open set Soft β-open set Soft pβα-open set Soft pβα-closed set Soft extremally disconnected.

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