کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5777859 | 1633051 | 2017 | 10 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Cross sections and pseudo-homomorphisms of topological abelian groups
ترجمه فارسی عنوان
مقاطع عرضی و شبه هومومورفیسم گروههای توپولوژی توپولوژی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
چکیده انگلیسی
We say that a mapping Ï between two topological abelian groups G and H is a pseudo-homomorphism if the associated map (x,y)âGÃGâ¦Ï(x+y)âÏ(x)âÏ(y)âH is continuous. This notion appears naturally in connection with cross sections (continuous right inverses for quotient mappings): given an algebraically splitting, closed subgroup H of a topological group X such that the projection Ï:XâX/H admits a cross section, one obtains a pseudo-homomorphism of X/H to H, and conversely. We show that H splits as a topological subgroup if and only if the corresponding pseudo-homomorphism can be decomposed as a sum of a homomorphism and a continuous mapping. We also prove that pseudo-homomorphisms between Polish groups satisfy the closed graph theorem. Several examples are given.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 228, 1 September 2017, Pages 285-293
Journal: Topology and its Applications - Volume 228, 1 September 2017, Pages 285-293
نویسندگان
H.J. Bello, M.J. Chasco, X. DomÃnguez,