کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4659512 | 1344326 | 2012 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Topological–algebraic properties of function spaces with set-open topologies
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
For a Tychonoff space X, we denote by Cλ(X) the space of all real-valued continuous functions on X with set-open topology. In this paper, we study the topological–algebraic properties of Cλ(X). Our main results state that (1) Cλ(X) is a topological vector space (a topological group) iff λ is a family of C-compact sets and Cλ(X)=Cλ′(X), where λ′ consists of all C-compact subsets of every set of λ. In particular, if Cλ(X) is a topological group, then the set-open topology coincides with the topology of uniform convergence on a family λ; (2) a topological group Cλ(X) is ω-narrow iff λ is a family of metrizable compact subsets of X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 159, Issue 3, 15 February 2012, Pages 800-805
Journal: Topology and its Applications - Volume 159, Issue 3, 15 February 2012, Pages 800-805