Free Product on Semihypergroups

TL;DR

This paper explores the construction of free products within the category of semihypergroups, demonstrating their effectiveness on a broad class of non-trivial examples, unlike in topological groups.

Contribution

It introduces a new approach to free products in semihypergroups, expanding understanding of their algebraic and topological structures.

Findings

Free product structures work well on many semihypergroups

Fails to produce free products for topological groups

Includes well-known examples like coset and orbit spaces

Abstract

In a previous paper [1] [MR4101040], we initiated a systematic study of semihypergroups and had a thorough discussion about some important analytic and algebraic objects associated to this class of objects. In this paper, we investigate free structures on the category of semihypergroups. We show that the natural free product structure along with the natural topology, although fails to give a free product for topological groups, works well on a vast non-trivial class of `pure' semihypergroups containing most of the well-known examples including non-trivial coset and orbit spaces.