The Connection between Topological and Algebraic Equivalence on Topological Hypergroups

Abstract

Based on the algebraic and topological structure of topological hypergroups, an important question arises. Does topological equivalence achieve algebraic equivalence and its converse?. The purpose of this paper is to show that this claim is false in general. By counterexample, we construct two finite topological hypergroups and define a bijective algebraic isomorphism between them that fails to be a homeomorphism. This example shows that additional conditions are required to establish any equivalence between algebraic and topological isomorphisms in topological hypergroups.