کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9516948 | 1633127 | 2005 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Hyperspaces of separable Banach spaces with the Wijsman topology
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let X be a separable metric space. By CldW(X), we denote the hyperspace of non-empty closed subsets of X with the Wijsman topology. Let FinW(X) and BddW(X) be the subspaces of CldW(X) consisting of all non-empty finite sets and of all non-empty bounded closed sets, respectively. It is proved that if X is an infinite-dimensional separable Banach space then CldW(X) is homeomorphic to (â) the separable Hilbert space â2 and FinW(X)âBddW(X)ââ2Ãâ2f, where â2f={(xi)iâNââ2|xi=0 except for finitely many iâN}. Moreover, we show that if the complement of any finite union of open balls in X has only finitely many path-components, all of which are closed in X, then FinW(X) and CldW(X) are ANR's. We also give a sufficient condition under which FinW(X) is homotopy dense in CldW(X).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 7-32
Journal: Topology and its Applications - Volume 148, Issues 1â3, 28 February 2005, Pages 7-32
نویسندگان
WiesÅaw KubiÅ, Katsuro Sakai, Masato Yaguchi,