کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661353 | 1344423 | 2007 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A pair of spaces of upper semi-continuous maps and continuous maps
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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 use ↓USC(X) and ↓C(X) to denote the families of the regions below all upper semi-continuous maps and of the regions below all continuous maps from X to I=[0,1], respectively. In this paper, we consider the spaces ↓USC(X) and ↓C(X) topologized as subspaces of the hyperspace Cld(X×I) consisting of all non-empty closed sets in X×I endowed with the Vietoris topology. We shall prove that ↓USC(X) is homeomorphic (≈) to the Hilbert cube Q=ω[−1,1] if and only if X is an infinite compact metric space. And we shall prove that (↓USC(X),↓C(X))≈(Q,c0), where , if and only if ↓C(X)≈c0 if and only if X is a compact metric space and the set of isolated points is not dense in X.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 8, 15 April 2007, Pages 1737-1747
Journal: Topology and its Applications - Volume 154, Issue 8, 15 April 2007, Pages 1737-1747