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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Topological–algebraic properties of function spaces with set-open topologies
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