Magma-valued metric spaces

TL;DR

This paper introduces magma-valued metric spaces and explores their properties, generalizing classical convergence and Cauchy sequence results using dense unital magmas and monoids.

Contribution

It develops the theory of magma-valued metric spaces and extends classical analysis results within this new algebraic framework.

Findings

Characterization of dense unital magmas and near-rings

Generalization of convergence and Cauchy properties

Analysis of magma-valued normed groups

Abstract

In the second section, we introduce dense unital magmas and show that a near-ring is dense if and only if it has a positive element smaller that unity. In the third section, we discuss magma-valued metric spaces. The density property of the ordered unital magmas and monoids helps us to generalize a couple of classical results related to the convergence and Cauchy property of sequences. The last section is devoted to magma-valued normed groups and some subgroups of the additive group of Cauchy sequences.