Topological distances and geometry over the symmetrized Omega algebra

Authors

  • Mesfer Alqahtani King Abdulaziz University
  • Cenap Özel King Abdulaziz University
  • Hanifa Zekraoui Larbi Ben M’hidi University

DOI:

https://doi.org/10.4995/agt.2020.13049

Keywords:

omega Algebra, dymmetrized Omega algebra, semidendrite, exponents, convex and topology

Abstract

The aim of this paper is to study some topological distances properties, semidendrites and convexity on th symmetrized omega algebra. Furthermore, some properties and exponents on the symmetrized omega algebra are introduced.

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Author Biographies

Mesfer Alqahtani, King Abdulaziz University

Department of Mathematics

Cenap Özel, King Abdulaziz University

Department of Mathematics

Hanifa Zekraoui, Larbi Ben M’hidi University

Department of Mathematics

References

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S. Khalid Nauman, C. Ozel and H. Zekraoui, Abstract Omega algebra that subsumes min and max plus algebras, Turkish Journal of Mathematics and Computer Science 11 (2019) 1-10.

G. L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: a brief introduction, Journal of Mathematical Sciences 140, no. 3 (2007), 426-444. https://doi.org/10.1007/s10958-007-0450-5

D. Maclagan and B. Sturmfels, Introduction to Tropical Geometry, Graduate Studies in Mathematics, vol. 161, American Mathematical Society, 2015. https://doi.org/10.1090/gsm/161

C. Ozel, A. Piekosz, E. Wajch and H. Zekraoui, The minimizing vector theorem in symmetrized max-plus algebra, Journal of Convex Analysis 26, no. 2 (2019), 661-686.

J.-E. Pin, Tropical semirings, Idempotency (Bristol, 1994), 50-69, Publ. Newton Inst., vol. 11, Cambridge Univ. Press, Cambridge, 1998. https://doi.org/10.1017/CBO9780511662508.004

I. Simon, Recognizable sets with multiplicities in the tropical semiring, in: Mathematical Foundations of Computer Science (Carlsbad, 1988), Lecture Notes in Computer Science, vol. 324, Springer, Berlin, 1988, pp. 107-120. https://doi.org/10.1007/BFb0017135

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Published

2020-10-01

How to Cite

[1]
M. Alqahtani, C. Özel, and H. Zekraoui, “Topological distances and geometry over the symmetrized Omega algebra”, Appl. Gen. Topol., vol. 21, no. 2, pp. 247–264, Oct. 2020.

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