Results 11 to 20 of about 147 (121)
Orderability and continuous selections for Wijsman and Vietoris hyperspaces [PDF]
Applied General Topology, 2003 Bertacchi and Costantini obtained some conditions equivalent to the existence of continuous selections for the Wijsman hyperspace of ultrametric Polish spaces. We introduce a new class of hypertopologies, the macro-topologies.
Debora Di Caprio, Stephen Watson
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Polishness of the Wijsman topology revisited [PDF]
Proceedings of the American Mathematical Society, 1998 Let X X be a completely metrizable space. Then the space of nonempty closed subsets of
Zsilinszky, Laszlo +1 more
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Applied General Topology, 2003 Recently it was shown that, in a metric space, the upper Wijsman convergence can be topologized with the introduction of a new far-miss topology. The resulting Wijsman topology is a mixture of the ball topology and the proximal ball topology.
Giuseppe Di Maio +2 more
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Applied General Topology, 2008 The subject of hyperspace topologies on closed or closed and compact subsets of a topological space X began in the early part of the last century with the discoveries of Hausdorff metric and Vietoris hit-and-miss topology.
Giuseppe Di Maio +2 more
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Fell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence [PDF]
Applied General Topology, 2001 We study the double Fell topology when this hypertopology is constructed over a quasi-pseudo-metric space. In particular, its relationship with the Wijsman hypertopology is studied.
Jesús Rodríguez-López
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Applied General Topology, 2003 We prove that the hyperspace of closed bounded sets with the Hausdor_ topology, over an almost convex metric space, is an absolute retract. Dense subspaces of normed linear spaces are examples of, not necessarily connected, almost convex metric spaces ...
Camillo Constantini, Wieslaw Kubís
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Three open problems on the Wijsman topology
, 2016 Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and other hyperspace topologies, and applications of the Wijsman topology in analysis have been explored.
Cao, J
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Coincidence of Vietoris and Wijsman topologies: A new proof [PDF]
, 1997 Summary: Let \((X,d)\) be a metric space and \(\text{CL}(X)\) the family of all nonempty closed subsets of \(X\). We provide a new proof of the fact that the coincidence of the Vietoris and Wijsman topologies induced by the metric \(d\) forces \(X\) to be a compact space.
Holá, L’.
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New Convergence Definitions for Sequences of Sets
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Several notions of convergence for subsets of metric space appear in the literature. In this paper, we define Wijsman I‐convergence and Wijsman I*‐convergence for sequences of sets and establish some basic theorems. Furthermore, we introduce the concepts of Wijsman I‐Cauchy sequence and Wijsman I*‐Cauchy sequence and then study their certain properties.
Ömer Kişi +2 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 11, Page 729-739, 2000., 2000 Approach uniformities were introduced in Lowen and Windels (1998) as the canonical generalization of both metric spaces and uniform spaces. This text presents in this new context of “quantitative” uniform spaces, a reflective completion theory which generalizes the well‐known completions of metric and uniform spaces. This completion behaves nicely with
Robert Lowen, Bart Windels
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