Some properties of s-paratopological groups

Abstract

A paratopological group G is called an s-paratopological
group if every sequentially continuous homomorphism from G to a paratopological group is continuous. For every paratopological groups (G,\tau), there is an s-coreflection (G,\tau_{S(G,\tau)}), which is an s-paratopological group. A characterization of s-coreflection of (G, \tau) is obtained, i.e., the topology \tau_{S(G,\tau)} is the finest paratopological group topology on G whose open sets are sequentially open in \tau. We prove that the class of Abelian s-paratopological groups is closed with open subgroups. The class of s-paratopological groups being determined by PT-sequences is particularly interesting. We show that this class of paratopological groups is closed with finite product, and give a characterization that two T-sequneces define the same paratopological group topology in Abelian groups. The s-sums of Abelian s-paratopological groups are defined. As applications, using s-sums we give characterizations of Abelian s-paratopological groups and Hausdorff Abelian s-paratopological groups, respectively.