Affiliation:
1. School of mathematics and statistics, Minnan Normal University, Zhangzhou, P.R. China
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, ?), there is an
s-coreflection (G, ?S(G,?)), which is an s-paratopological group. A
characterization of s-coreflection of (G, ?) is obtained, i.e., the topology
?S(G,?) is the finest paratopological group topology on G whose open sets
are sequentially open in ?. 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.
Publisher
National Library of Serbia
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