Separation Axioms on Upper Sets of BE-Algebras

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DOI: https://doi.org/10.28924/2291-8639-24-2026-138
Published: Apr 30, 2026
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Maliwan Phattarachaleekul, Separation Axioms on Upper Sets of BE-Algebras, Int. J. Anal. Appl., 24 (2026), 138.

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Maliwan Phattarachaleekul

Abstract

This paper investigates the topological properties of upper sets in \(BE\)-algebras by introducing three novel separation axioms \(BET_0\), \(BET_1\), and \(BET_2\) inspired by the classical \(T_0\), \(T_1\), and \(T_2\) 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 \(A(x, y) = \{ z \in X \mid x * (y * z) = 0 \}\). 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 \(BET_i\)-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.

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