Quotient of Topological Ternary Semigroup

TL;DR

This paper introduces a quotient construction for topological ternary semigroups, establishing conditions for the quotient to retain semigroup or group structures within the topological setting.

Contribution

It defines a congruence-based quotient structure on topological ternary semigroups and identifies conditions for it to form a topological ternary semigroup or group.

Findings

Established conditions for quotient to be a topological ternary semigroup.

Derived criteria for the quotient to be a topological ternary group.

Extended results to cases where the base structure is a topological ternary group.

Abstract

In this paper we introduce a quotient structure on topological ternary semigroup by defining a congruence suitably. We have found conditions under which this quotient structure becomes a topological ternary semigroup. We have also obtained conditions that make this quotient a topological ternary group, whenever the base structure is a topological ternary group.