Uniform Continuity on Bounded Sets and the Attouch-Wets Topology

DOI10.2307/2048503zbMath0677.54007OpenAlexW4239210854MaRDI QIDQ3833231

Anna Di Concilio, Gerald A. Beer

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2048503

zbMATH Keywords

set convergencebounded Hausdorff topologymetrizable Attouch-Wets topologytopology of uniform convergence of distance functionalsuniform continuity on bounded sets

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20)

Related Items

Well-posed optimization problems and a new topology for the closed subsets of a metric space ⋮ Some notes on induced functions and group actions on hyperspaces ⋮ Wijsman convergence: A survey ⋮ A splitting property of the upper bounded-Hausdorff convergence ⋮ On the Fell topology ⋮ Polar locally convex topologies and Attouch-Wets convergence ⋮ Wijsman topology on function spaces ⋮ Wijsman convergence of convex sets under renorming ⋮ The Wijsman and Attouch-Wets topologies on hyperspaces revisited ⋮ Simultaneous extension of continuous and uniformly continuous functions ⋮ Gap topologies in metric spaces ⋮ A question related to the Isbell problem ⋮ Uniform continuity, uniform convergence, and shields ⋮ Topologies and convergences on the space of convex functions ⋮ The bornology of cofinally complete subsets ⋮ Uniformizing (proximal) \(\varDelta\)-topologies. ⋮ Graphical convergence of continuous functions ⋮ Bornological convergences on the hyperspace of a uniformizable space ⋮ Bornological convergences and local proximity spaces ⋮ Convergence of partial maps ⋮ Arzelà's theorem and strong uniform convergence on bornologies ⋮ Boundedly UC spaces and topologies on function spaces ⋮ Strong uniform continuity ⋮ Weak Topologies for the Closed Subsets of a Metrizable Space ⋮ Total boundedness and bornologies ⋮ Testing concerning the homogeneity of some predator-prey populations ⋮ Comparability of lower Attouch-Wets topologies ⋮ Metrics that generate the same hyperspace convergence ⋮ On local versions of metric uc-ness, hypertopologies and function space topologies

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