کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661186 | 1344413 | 2006 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The hyperspace of the regions below of continuous maps is homeomorphic to c0
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
For a compact metric space (X,d), we use ↓USC(X) and ↓C(X) to denote the families of the regions below of all upper semi-continuous maps and the regions below of all continuous maps from X to I=[0,1], respectively. In this paper, we consider the two spaces 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 show that ↓C(X) is Baire if and only if the set of isolated points is dense in X, but ↓C(X) is not a Gδσ-set in ↓USC(X) unless X is finite. As the main result, we shall prove that if X is an infinite locally connected compact metric space then (↓USC(X),↓C(X))≈(Q,c0), where Q=ω[−1,1] is the Hilbert cube and .
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issue 15, 1 September 2006, Pages 2908-2921
Journal: Topology and its Applications - Volume 153, Issue 15, 1 September 2006, Pages 2908-2921