- Tytuł:
- Spaces of upper semicontinuous multi-valued functions on complete metric spaces
- Autorzy:
-
Sakai, Katsuro
Uehara, Shigenori - Powiązania:
- https://bibliotekanauki.pl/articles/1205236.pdf
- Data publikacji:
- 1999
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
space of upper semicontinuous multi-valued functions,
hyperspace of non-empty closed sets,
Hausdorff metric,
Hilbert space,
uniformly locally connected - Opis:
- Let X = (X,d) be a metric space and let the product space X × ℝ be endowed with the metric ϱ ((x,t),(x',t')) = max{d(x,x'), |t - t'|}. We denote by $USCC_B(X)$ the space of bounded upper semicontinuous multi-valued functions φ : X → ℝ such that each φ(x) is a closed interval. We identify $φ ∈ USCC_B(X)$ with its graph which is a closed subset of X × ℝ. The space $USCC_B(X)$ admits the Hausdorff metric induced by ϱ. It is proved that if X = (X,d) is uniformly locally connected, non-compact and complete, then $USCC_B(X)$ is homeomorphic to a non-separable Hilbert space. In case X is separable, it is homeomorphic to $ℓ_2(2^ℕ)$.
- Źródło:
-
Fundamenta Mathematicae; 1999, 160, 3; 199-218
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł