Separation Axioms on Upper Sets of BE-Algebras

Paper Details

Authors: Phattarachaleekul M.

DOI: 10.28924/2291-8639-24-2026-138

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

This paper investigates the topological properties of upper sets in BE-algebras by introducing three novel separation axioms BET0, BET1, and BET2 inspired by the classical T0, T1, and T2 separation axioms in general topology. Using the structure of BE-algebras and their induced upper sets, we define a topology generated by a subbasis of sets of the form A(x, y) = {z ∈ X | x ∗ (y ∗ z) = 0}. We establish the necessary and sufficient conditions for a BE-space to satisfy each of these axioms. Several illustrative examples are provided to demonstrate the distinctions among the BETi-spaces. Furthermore, we examine interrelations among the axioms and their implications for algebraic structures, such as involutory BE-algebras and fuzzy ideals. Our results contribute to the integration of algebraic and topological concepts, offering new insights into the study of BE-structured spaces. © 2026 the author(s).

Keywords

BE-algebras; BE-space; BE-structure; BET₀-space; BET₁-space; BET₂-space; Upper sets

Read Paper Back to Search