کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8899837 | 1631551 | 2018 | 19 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Stone-Weierstrass and extension theorems in the nonlocally convex case
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
In the general (nonlocally convex) case we prove a Stone-Weierstrass-type theorem for sets of continuous vector-valued functions on Hausdorff topological spaces whose compact subsets have finite Lebesgue covering dimension (topological dimension). For such topological space T and Hausdorff topological vector space X (real or complex), in the presence of a separating set of multipliers, the theorem characterizes the closure of a subset in: C(T,X) (resp. C0(T,X) and Cb(T,X)), endowed with the compact-open topology (respectively, the uniform convergence topology and the strict topology). Applications include a Stone-Weierstrass theorem for vector subspaces, range-support uniform approximation results (under constraints on both the range and the support of the approximant function), extension theorems for vector-valued functions, and a short proof of a Schauder-type fixed point theorem. Our noncompact version of the Stone-Weierstrass theorem has significant consequences, among which we mention the extension theorem for vector-valued functions defined on closed subsets of paracompact spaces.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 462, Issue 2, 15 June 2018, Pages 1536-1554
Journal: Journal of Mathematical Analysis and Applications - Volume 462, Issue 2, 15 June 2018, Pages 1536-1554
نویسندگان
Vlad Timofte, Aida Timofte, Liaqat Ali Khan,