Scholarly Article

The Connection between Topological and Algebraic Equivalence on Topological Hypergroups

Mariam Gassar, AbouElwan, Yasser

2026-02-15 · AlQalam Journal of Medical and Applied Sciences · University of Tripoli Alahlia

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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.

Keywords

Hypergroup, Topological group, Topological hypergroup, Isomorphism of topological hyper group.

Citation Details

AlQalam Journal of Medical and Applied Sciences, Vol. 9, No. 2, pp. 429-431