2013
DOI: 10.1016/j.topol.2013.08.001
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Factorization properties of paratopological groups

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Cited by 24 publications
(13 citation statements)
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“…A similar result on a regular paratopological group was proved in [4,Lemma 3.18]. In [8,Lemma 4.1], it was proved that if P is a G δ -set of a Lindelöf totally ω-narrow T 1 paratopological group G and e ∈ P , where e is the neutral element of G, then there is a closed invariant subgroup N of G such that N ⊂ P and G/N is a paratopological group with countable pseudocharacter. Since a totally ω-narrow paratopological group is ω-balanced [4, Proposition 3.8] and a Lindelöf T 1 paratopological group has countable symmetry number [5, Proposition 2.4], we get a similar result on an ω-balanced paratopological group G with Sm(G) ≤ ω.…”
Section: Proof By Corollary 8 We Know Thatsupporting
confidence: 74%
“…A similar result on a regular paratopological group was proved in [4,Lemma 3.18]. In [8,Lemma 4.1], it was proved that if P is a G δ -set of a Lindelöf totally ω-narrow T 1 paratopological group G and e ∈ P , where e is the neutral element of G, then there is a closed invariant subgroup N of G such that N ⊂ P and G/N is a paratopological group with countable pseudocharacter. Since a totally ω-narrow paratopological group is ω-balanced [4, Proposition 3.8] and a Lindelöf T 1 paratopological group has countable symmetry number [5, Proposition 2.4], we get a similar result on an ω-balanced paratopological group G with Sm(G) ≤ ω.…”
Section: Proof By Corollary 8 We Know Thatsupporting
confidence: 74%
“…Further, by Theorem 2.3, from the fact that T 2 (G) is simply sm-factorizable it follows that there are a sub-sm-paratopological group H, a continuous homomorphism h of T 2 (G) onto H and a continuous function g : Let G sr be simply sm-factorizable. Take any continuous function f : G → R. Then by [17,Lemma 3.5] f is also continuous on G sr , and therefore, there are a sub-smparatopological group H, a continuous homomorphism h of G sr onto H and a continuous function g :…”
Section: Characterizations Of Simply Sm-factorizable (Para)topologicamentioning
confidence: 99%
“…The relations between the properties of an almost topological group G and the underlying topological group G are not completely clear. We present here only one question in this respect (for the concept of R-factorizability, see [2,Chapter 8] and [12,15]). Question 7.2.…”
Section: Some Questionsmentioning
confidence: 99%