The concept of gyrogroups is a generalization groups which do not explicitly have associativity. Recently, Atiponrat extended the idea topological (paratopological) to gyrogroups. In this paper, we prove that every regular (Hausdorff) locally gyroscopic invariant paratopological gyrogroup G completely (function Hausdorff). These results improve theorems Banakh and Ravsky for groups. Also, exten...

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

A unified internal characterization of exponential objects in the categories of topological, pretopological and paratopological spaces (with continuous maps) is presented as an application of a theorem on product of Dcompactoid filters. Résumé: Une caractérisation unifiée des objets exponentiels dans les catégories des espaces topologiques, prétopologiques et paratopologiques (munies des applic...