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...

A subset S of a paratopological group G is suitable set for G, if discrete subspace $$S\cup \{e\}$$ ∪ { e } closed, and the subgroup $$\langle S\rangle $$ ⟨ ⟩ generated by dense in G. Suitable sets topological groups were studied many authors. The aim present paper to provide start-up general investigation groups, looking what extent we can (by proving propositions) or cannot constructing examp...