On convergence of closed sets in a metric space and distance functions

DOI10.1017/S0004972700009370zbMath0558.54007MaRDI QIDQ3223517

Gerald A. Beer

Publication date: 1985

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Function spaces in general topology (54C35) Convergence and divergence of series and sequences of functions (40A30) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20)

Related Items (40)

Boundary regularity and stability for spaces with Ricci bounded below ⋮ Asymptotically lacunary statistical equivalence of double sequences of sets ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Lacunary statistical convergence of double sequences of sets ⋮ DOUBLE WIJSMAN LACUNARY STATISTICAL CONVERGENCE OF ORDER 𝛼 ⋮ On summability of sequences of sets by Cesàro submethod ⋮ Space of continuous set-valued mappings with closed unbounded values ⋮ λ− Wijsman statistical convergence on time scales ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Wijsman Orlicz asymptotically ideal \(\phi\)-statistical equivalent sequences ⋮ Unnamed Item ⋮ Vector optimization problems via improvement sets ⋮ Unnamed Item ⋮ New results in the theory of multivalued mappings. I: Topological characteristics and solvability of operator relations ⋮ Pointwise differentiability of higher order for sets ⋮ On Wijsman \(\mathcal{I}_{2}\)-lacunary statistical convergence for double set sequences ⋮ ON λ-ASYMPTOTICALLY WIJSMAN GENERALIZED STATISTICAL CONVERGENCE OF SEQUENCES OF SETS ⋮ Density by moduli and Wijsman lacunary statistical convergence of sequences of sets ⋮ On asymptotically Wijsman lacunary statistical convergence of set sequences in ideal context ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An extension of asymptotically lacunary statistical equivalence set sequences ⋮ Distance functionals and suprema of hyperspace topologies ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Wijsman lacunary \(\mathcal{I}\)-invariant convergence of sequences of sets ⋮ Unnamed Item ⋮ New convergence definitions for sequences of sets ⋮ On Kuratowski I-convergence of sequences of closed sets ⋮ SOME STATISTICAL CONVERGENCE TYPES OF ORDER $\alpha$ FOR DOUBLE SET SEQUENCES ⋮ Unnamed Item ⋮ Wijsman asymptotic lacunary \(\mathcal{I}_2\)-invariant equivalence for double set sequences ⋮ Unnamed Item ⋮ Curvature measures and soap bubbles beyond convexity ⋮ Metric regularity and Lyusternik-Graves theorem via approximate fixed points of set-valued maps in noncomplete metric spaces

Cites Work

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• Successive approximation and linear stability involving convergent sequences of optimization problems
• Convex analysis and measurable multifunctions
• Hausdorffsche Metrik und Approximationen
• On a generalization of Jackson's theorem for best approximation
• More on Convergence of Continuous Functions and Topological Convergence of Sets
• On the Convergence of Sequences of Convex Sets in Finite Dimensions
• Preservation of Convergence of Convex Sets and Functions in Finite Dimensions
• On Uniform Convergence of Continuous Functions and Topological Convergence of Sets
• Cone Lattices of Upper Semicontinuous Functions
• Convergence of Functions: Equi-Semicontinuity
• Convergence of Sequences of Convex Sets, Cones and Functions. II
• Graph Topology for Function Spaces

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