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...

bentea and tu{a}rnu{a}uceanu~(an. c{s}tiinc{t}. univ. al. i.cuza iac{s}, ser. nouv{a}, mat., {bf 54(1)} (2008), 209-220)proposed the following problem: find an explicit formula for thenumber of fuzzy subgroups of a finite hamiltonian group of type$q_8times mathbb{z}_n$ where $q_8$ is the quaternion group oforder $8$ and $n$ is an arbitrary odd integer. in this paper weconsider more general grou...

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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...