Factorization properties of paratopological groups

摘要

In this article we continue the study of R-factorizability in paratopological groups. It is shown that: (1) all concepts of R-factorizability in paratopological groups coincide; (2) a Tychonoff paratopological group G is R-factorizable if and only if it is totally ω-narrow and has property ω-QU; (3) every subgroup of a T_1 paratopological group G is R-factorizable provided that the topological group G~* associated to G is a Lindeloef ∑-space, i.e., G is a totally Lindeloef ∑-space; (4) if ∏ =∏_(i∈l) G_i product of T_1 paratopological groups which are totally Lindeloef ∑-spaces, then each dense subgroup of ∏ is R-factorizable. These results answer in the affirmative several questions posed earlier by M. Sanchis and M. Tkachenko and by S. Lin and L.-H. Xie.