کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778076 | 1633063 | 2017 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Three-space properties in paratopological groups
ترجمه فارسی عنوان
خواص سه فضایی در گروه های پاراتوپولوژیک
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
We show that neither first-countable nor second-countable are three-space properties in the class of paratopological groups: we present a countable regular paratopological Abelian group H which contains a closed discrete subgroup F such that H/F is topologically isomorphic to the rational numbers with the Sorgenfrey topology and H is not first-countable. Also, we prove that if H is an invariant topological subgroup of a paratopological group G such that H is second-countable and G/H has countable network, then G has countable network as well (this answers a question posed in [12]). Hence if H is an invariant topological subgroup of a first-countable paratopological group G such that H and G/H are second-countable, then so is G.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 216, 1 February 2017, Pages 74-78
Journal: Topology and its Applications - Volume 216, 1 February 2017, Pages 74-78
نویسندگان
Manuel Fernández, Iván Sánchez,