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
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات هندسه و توپولوژی
پیش نمایش صفحه اول مقاله
Hyperspaces of separable Banach spaces with the Wijsman topology
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 (≈) the separable Hilbert space ℓ2 and FinW(X)≈BddW(X)≈ℓ2×ℓ2f, where ℓ2f={(xi)i∈N∈ℓ2|xi=0 except for finitely many i∈N}. 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 1–3, 28 February 2005, Pages 7-32
نویسندگان
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