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An embedding in the Fell topology [PDF]
Topology and its Applications, 2015 It is shown that if a $T_2$ topological space contains an uncountable closed discrete set, then $ _1 \times ( _1 + 1)$ embeds as a closed subspace of $(CL(X), _F)$, the hyperspace of nonempty closed subsets of $X$ equipped with the Fell topology.
L. Holá
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Fell topology and its application for some semidirect products
Annals of Functional Analysis, 2022 Let \(G\) be a locally compact and \(\widehat{G}\) the unitary dual considered with the Fell topology. The cortex of \(G\), denoted by \(\mathrm{cor}(G)\) is the collection of \(\pi \in \widehat{G}\) that can not be separated from the trivial representation of \(G\). In the paper under review, the authors consider \(G = K \ltimes \mathbb H_d\) where \(\
Regeiba, Hedi +2 more
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Topological classification of function spaces with the Fell topology I
Topology and its Applications, 2014 Let \(X\) be a Tychonoff topological space, \(L\) a subset of the real line \(\mathbb R\) with the usual order and topology, and \(USC(X, L)\) (respectively, \(C(X, L)\)) the set of all upper semi-continuous maps (respectively, continuous maps) from \(X\) to the subspace \(L\) of \(\mathbb R\).
Yang, Zhongqiang, Yan, Pengfei
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Normality and paracompactness of the Fell topology [PDF]
Proceedings of the American Mathematical Society, 1999 Let X X be a Hausdorff topological space and C L ( X ) CL(X) the hyperspace of all closed nonempty subsets of X X . We show that the Fell topology on C L ( X ) CL(X) is normal if and only if the space X
Holà, L., Levi, S, Pelant, J
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An embedding theorem for the Fell topology.
Michigan Mathematical Journal, 1988 Let X be a metric space, and let CL(X) be the set of all nonempty closed subsets of X. It is known that, when the metric d on X is bounded, \(E\mapsto d(\cdot,E)\) defines an embedding of CL(X) with the Hausdorff metric topology into the space of bounded continuous real-valued functions on X with the topology of uniform convergence.
G. Beer
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Weak Convergence of Probability Measures on Hyperspaces with the Upper Fell-Topology [PDF]
Bulletin of the Iranian Mathematical SocietyAbstractLet E be a locally compact second countable Hausdorff space and $$\mathcal {F}$$ F the pertaining family of all closed sets. We endow $$\mathcal {F}$$ F respectively with the Fell-topology, the upper Fell topology or the upper Vietoris-topology and investigate weak ...
Dietmar Ferger
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Set-Valued Analysis, 1993 The author characterizes the first and second countability of the Fell hypertopology in terms of the properties of the base space. He then compares the convergence in Fell topology to that in the Attouch-Wets topology. Applications are indicated. As with the author's other writings, the paper is pleasant to read.
G. Beer
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Selection principles of the Fell topology and the Vietoris topology
Topology and its Applications, 2016 For a noncompact Hausdorff space \(X\), let \(\text{CL} (X)\) be the family of all nonempty closed subsets of \(X\). Let \(\tau _F\) (resp., \(\tau_V\)) denote the Fell (resp., Vietoris) topology on \(\text{CL} (X)\). Motivated by \textit{G. Di Maio} et al. [Topology Appl. 153, No. 5--6, 912--923 (2005; Zbl 1087.54007)], the author investigates several
Zuquan Li
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Baire category properties of function spaces with the Fell hypograph topology [PDF]
Topology and its Applications, 2019 For a Tychonoff space $X$ and a subspace $Y\subset\mathbb R$, we study Baire category properties of the space $C_{\downarrow F}(X,Y)$ of continuous functions from $X$ to $Y$, endowed with the Fell hypograph topology. We characterize pairs $X,Y$ for which the function space $C_{\downarrow F}(X,Y)$ is $\infty$-meager, meager, Baire, Choquet, strong ...
Wang, Leijie, Banakh, Taras
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The Spaces of Closed Convex Sets in Euclidean Spaces with the Fell Topology [PDF]
Bulletin of the Polish Academy of Sciences Mathematics, 2007 Let ConvF (R) be the space of all non-empty closed convex sets in Euclidean space R endowed with the Fell topology. In this paper, we prove that ConvF (R) ≈ R × Q for every n > 1 whereas ConvF (R) ≈ R× I. Let Conv(X) be the set of all non-empty closed convex sets in a normed linear space X = (X, ‖·‖). We can consider various topologies on Conv(X).
Katsuro Sakai, Zhongqiang Yang
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