On Metric Quasigroups and Metric Loops

Abstract

Metric space is a set in which a notion of distance between elements is defined in a precise and consistent way. Metric space provides a general and flexible framework for studying the idea of distance which underlies much of mathematics and its applications. In 1922, Stefan Banach was able to use the space alongside with contraction to prove the existence and uniqueness of solutions of ODE. This study opened the eyes of many researchers to this area of study. In this paper, we introduce the concept of metric quasigroups and metric loop with examples. This will enrich the space. We also introduce homomorphism in this concept. Our work unify, extend and generalize existing work in literature.