Results 1 to 10 of about 975 (166)
On metrization of the hit-or-miss topology using Alexandroff compactification
International Journal of Approximate Reasoning, 2007 The authors consider the hyperspace \(\mathcal F(E)\) of closed subsets of a Hausdorff topological space \(E\), endowed with the so-called Fell topology \(\tau_f\) (termed hit-or-miss topology in the paper) having subbase elements of the form \(\{A\in\mathcal F(E): A\cap U\neq\emptyset\}\) and \(\{A\in\mathcal F(E): A\cap K=\emptyset\}\), where \(U ...
Yangeng Wang
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Note on hit-and-miss topologies
Rendiconti Del Circolo Matematico Di Palermo, 2000 The author continues his paper [Rend. Circ. Mat. Palermo, II. Ser. 45, No. 1, 75-83 (1996; Zbl 0907.54010)], concerning hit-and-miss topologies on the set \(\text{Cl}(X)\) of nonempty closed subsets of a topological space \(X\), taking always closed sets to produce the hit-and-miss basic open sets (\(\Delta\)-topologies).
László Zsilinszky
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Hurewicz and Hurewicz-type star selection principles for hit-and-miss topology
Filomat, 2023 In this paper we continue the study of the characterization of selection principles in the hyperspaces CL(X), K(X), F(X) and CS(X), endowed with the hit-and-miss topology, by using ??(?)-networks and c?(?)-covers of a topological space X. Specifically, we prove theorems which characterize the covering properties Hurewicz, strongly star ...
Ricardo Cruz-Castillo +2 more
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The infimal value functional and the uniformization of hit-and-miss hyperspace topologies [PDF]
Proceedings of the American Mathematical Society, 1994 We give necessary and sufficient conditions for the uniformizability of hit-and-miss and proximal hit-and-miss hyperspace topologies defined on the nonempty closed subsets CL
Beer, Gerald, Tamaki, Robert
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All hypertopologies are hit-and-miss
Applied General Topology, 2002 We solve a long standing problem by showing that all known hypertopologies are hit-and-miss. Our solution is not merely of theoretical importance.
Somshekhar Naimpally
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Topological dynamics on hyperspaces
Applied General Topology, 2010 In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the ...
Puneet Sharma, Anima Nagar
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Uniformly discrete hit-and-miss hypertopology. A missing link in hypertopologies
Applied General Topology, 2006 Recently it was shown that the lower Hausdorff metric (uniform) topology is generated by families of uniformly discrete sets as hit sets. This result leads to a new hypertopology which is the join of the above topology and the upper Vietoris topology ...
Giuseppe Di Maio +2 more
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A short note on hit-and-miss hyperspaces
Applied General Topology, 2003 Based on some set-theoretical observations, compactness results are given for general hit-and-miss hyperspaces. Compactness here is sometimes viewed splitting into “κ-Lindelöfness” and “κ-compactness” for cardinals κ.
René Bartsch, Harry Poppe
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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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