کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4658236 1633086 2015 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On topological properties of Fréchet locally convex spaces with the weak topology
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
On topological properties of Fréchet locally convex spaces with the weak topology
چکیده انگلیسی

We describe the topology of any cosmic space and any ℵ0ℵ0-space in terms of special bases defined by partially ordered sets. Using this description we show that a Baire cosmic group is metrizable. Next, we study those locally convex spaces (lcs) E   which under the weak topology σ(E,E′)σ(E,E′) are ℵ0ℵ0-spaces. For a metrizable and complete lcs E   not containing (an isomorphic copy of) ℓ1ℓ1 and satisfying the Heinrich density condition we prove that (E,σ(E,E′))(E,σ(E,E′)) is an ℵ0ℵ0-space if and only if the strong dual of E is separable. In particular, if a Banach space E   does not contain ℓ1ℓ1, then (E,σ(E,E′))(E,σ(E,E′)) is an ℵ0ℵ0-space if and only if E′E′ is separable. The last part of the paper studies the question: Which spaces (E,σ(E,E′))(E,σ(E,E′)) are ℵ0ℵ0-spaces? We extend, among the others, Michael's results by showing: If E is a metrizable lcs or a (DF  )-space whose strong dual E′E′ is separable, then (E,σ(E,E′))(E,σ(E,E′)) is an ℵ0ℵ0-space. Supplementing an old result of Corson we show that, for a Čech-complete Lindelöf space X the following are equivalent: (a) X   is Polish, (b) Cc(X)Cc(X) is cosmic in the weak topology, (c) the weak⁎weak⁎-dual of Cc(X)Cc(X) is an ℵ0ℵ0-space.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 192, 1 September 2015, Pages 123–137
نویسندگان
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