Factorization properties of paratopological groups |
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Authors: | Li-Hong Xie Shou Lin Mikhail Tkachenko |
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Institution: | 1. School of Mathematics, Sichuan University, Chengdu 610065, PR China;2. Institute of Mathematics, Ningde Normal University, Ningde 352100, PR China;3. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Av. San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340, México, D.F., Mexico |
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Abstract: | 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 T1 paratopological group G is R-factorizable provided that the topological group G? associated to G is a Lindelöf Σ-space, i.e., G is a totally Lindelöf Σ-space ; (4) if Π=∏i∈IGi is a product of T1 paratopological groups which are totally Lindelöf Σ-spaces, then each dense subgroup of Π 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. |
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Keywords: | primary 22A30 54H10 secondary 54D30 54A25 |
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