Some properties of s-paratopological groups

Zhongbao Tang ; Mengna Chen

Filomat, Tome 37 (2023) no. 26, p. 8941

Résumé

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, τ), there is an s-coreflection (G, τ S(G,τ)), which is an s-paratopological group. A characterization of s-coreflection of (G, τ) is obtained, i.e., the topology τ S(G,τ) is the finest paratopological group topology on G whose open sets are sequentially open in τ. 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-sequences 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.

Détail

DOI : 10.2298/FIL2326941T

Classification : 54A20, 22A30, 54B15, 54C10
Keywords: s-paratopological group, sequentially continuous, PT-sequence, sequential coreflection, sequence-covering mapping