کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4658248 | 1633085 | 2015 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On uniform spaces with a small base and K -analytic Cc(X)Cc(X) spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
A base {Uα:α∈NN}{Uα:α∈NN} of a uniformity is a GG-base if Uβ⊆UαUβ⊆Uα whenever α≤βα≤β. If X is a completely regular space we show that there exists an admissible uniformity on X with a GG-base that contains the Nachbin uniformity if and only if there exists a resolution of the space Cc(X)Cc(X) of real-valued continuous functions on X equipped with the compact-open topology consisting of equicontinuous sets. This result is applied to show, among other things, that if G is a kRkR-space topological group such that Cc(G)Cc(G) is K-analytic then G has a GG-base. In the opposite direction, if G is a topological group with a GG-base and enjoys the so-called property U , then Cc(G)Cc(G) has a resolution consisting of equicontinuous sets.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 193, 15 September 2015, Pages 77–83
Journal: Topology and its Applications - Volume 193, 15 September 2015, Pages 77–83
نویسندگان
Juan Carlos Ferrando,