The Extended Metric Space on Max-Plus Algebra

Lalu Riski Wirendra Putra; Qurratul Aini; Muhammad Rijal Alfian

doi:10.29303/emj.v8i1.254

Authors

Lalu Riski Wirendra Putra Department of Mathematics, Universitas Mataram, Indonesia
Qurratul Aini Department of Mathematics, Universitas Mataram, Indonesia
Muhammad Rijal Alfian Department of Mathematics, Universitas Mataram, Indonesia

DOI:

https://doi.org/10.29303/emj.v8i1.254

Keywords:

Max Plus Algebra, metric space, sequence, convergrence

Abstract

Max-Plus Algebra is the newly emerged mathematical object as one of the algebraic structures. Max Plus Algebra is a semi-ring with the maximum operation as its addition and the plus operation as its multiplication. In 2012, Carl et.al. established a novel notion about metric in max-plus geometry which is the semi-module over the semi-ring with maximum and addition biner operations. The writer researched to discover the distance function or metric, especially for the extended real-valued metric of Max-Plus Algebra and its properties with maximum and addition biner operations. By using both direct and indirect proof methods, the distance function of Max Plus Algebra and its topological properties were obtained.

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