Separation Axioms on Upper Sets of BE-Algebras

Phattarachaleekul, Maliwan

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

Research Article

Separation Axioms on Upper Sets of BE-Algebras

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.

How to Cite

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

BibTeX

@article{Phattarachaleekul2026,
  author  = {Phattarachaleekul, Maliwan},
  title   = {Separation Axioms on Upper Sets of BE-Algebras},
  journal = {Int. J. Anal. Appl.},
  volume  = {24},
  year    = {2026},
  pages   = {138},
  doi     = {10.28924/2291-8639-24-2026-138}
}

References

[1] T. Noiri, V. Popa, A Generalized of Some Forms of g-Irresolute Functions, Eur. J. Pure Appl. Math. 4 (2009), 473–493.
[2] C. Boonpok, Biminimal Structure Spaces, Int. Math. Forum 5 (2010), 703–707.
[3] M. Tunapan, Some Separation Axioms in Biminimal Structure Spaces, Int. Math. Forum 5 (2010), 2425–2428. https://www.researchgate.net/publication/268068272.
[4] S.S. Ahn, K.S. So, On Ideals and Upper Sets in BE-Algebras, Sci. Math. Jpn. 68 (2008), 279–-285. https://doi.org/10.32219/isms.68.2_279.
[5] S.S. Ahn, K.S. So, On Generalized Upper Sets in BE-Algebras, Bull. Korean Math. Soc. 46 (2009), 281–287. https://doi.org/10.4134/BKMS.2009.46.2.281.
[6] Z. Çiloğlu, Y. Çeven, Commutative and Bounded Be-Algebras, Algebra 2013 (2013), 473714. https://doi.org/10.1155/2013/473714.
[7] H.S. Kim, Y.H. Kim, On BE-Algebras, Sci. Math. Jpn. 66 (2007), 113–116.
[8] H.S. Kim, K.J. Lee, Extended Upper Sets in BE-Algebras, Bull. Malays. Math. Sci. Soc. (2) 34 (2011), 511–520.
[9] S. Mehrshad, J. Golzarpoor, On Topological BE-Algebras, Math. Morav. 21 (2017), 1–13.
[10] A. Rezaei, A.R. Seied, R.A. Borzooei, Relation between Hilbert Algebras and BE-Algebras, Appl. Appl. Math.: Int. J. 8 (2013), 573–584.