Weak Topologies for the Closed Subsets of a Metrizable Space

DOI10.2307/2154406zbMath0810.54011OpenAlexW4237878889MaRDI QIDQ4038499

Roberto Lucchetti, Gerald A. Beer

Publication date: 16 May 1993

Full work available at URL: https://doi.org/10.2307/2154406

zbMATH Keywords

weak topologyHausdorff metricVietoris topologyFell topologyWijsman topologyAttouch-Wets topologyMosco topologydistance functionallocally finite topologyproximal topology

Mathematics Subject Classification ID

Real- or complex-valued set functions (28A10) Hyperspaces in general topology (54B20) Continuous maps (54C05)

Related Items (32)

Well-posed optimization problems and a new topology for the closed subsets of a metric space ⋮ Stability of the geometric Ekeland variational principle: Convex case ⋮ Wijsman convergence: A survey ⋮ Classical set convergences and topologies ⋮ Set convergences: A survey and a classification ⋮ On Hypertopologies ⋮ Stability of constrained optimization problems ⋮ On the Fell topology ⋮ Bornological convergences ⋮ Unnamed Item ⋮ More on the behaviors of fixed points sets of multifunctions and applications ⋮ Well-set and well-posed minimization problems ⋮ A representation theorem for quasi-metric spaces ⋮ Equivalence among hypertopologies ⋮ Wijsman convergence of convex sets under renorming ⋮ Lipschitz Regularization and the Convergence of Convex Functions ⋮ On the Infimum of the Hausdorff and Vietoris Topologies ⋮ The Wijsman and Attouch-Wets topologies on hyperspaces revisited ⋮ Gap topologies in metric spaces ⋮ Constrained convex optimization problems-well-posedness and stability^* ⋮ Nature-inspired framework for measuring visual image resemblance: a near rough set approach ⋮ Properties related to first countability and countable compactness in hyperspaces: A new approach. ⋮ Set Convergences. An Attempt of Classification ⋮ \(\mathcal S\)-topologies and bounded convergences ⋮ Bornological convergences on the hyperspace of a uniformizable space ⋮ Efficiency and the uniform linear minorization of convex functions ⋮ The Infimal Value Functional and the Uniformization of Hit-and-Miss Hyperspace Topologies ⋮ Weak topology and Browder--Kirk's theorem on hyperspace ⋮ Gap, excess and bornological convergence ⋮ Slice convergence: stabilité et optimisation dans les espaces non réflexifs ⋮ Metrics that generate the same hyperspace convergence ⋮ Convergence of epigraphs and of sublevel sets

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