کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4620196 | 1339456 | 2009 | 7 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Embeddings and frames of function spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
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چکیده انگلیسی
For every Tychonoff space X we denote by Cp(X) the set of all continuous real-valued functions on X with the pointwise convergence topology, i.e., the topology of subspace of RX. A set P is a frame for the space Cp(X) if Cp(X)⊂P⊂RX. We prove that if Cp(X) embeds in a σ-compact space of countable tightness then X is countable. This shows that it is natural to study when Cp(X) has a frame of countable tightness with some compactness-like property. We prove, among other things, that if X is compact and the space Cp(X) has a Lindelöf frame of countable tightness then t(X)⩽ω. We give some generalizations of this result for the case of frames as well as for embeddings of Cp(X) in arbitrary spaces.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 357, Issue 1, 1 September 2009, Pages 237-243
Journal: Journal of Mathematical Analysis and Applications - Volume 357, Issue 1, 1 September 2009, Pages 237-243