Wijsman topology on function spaces
type: Item
instance of: scholarly article
title: Wijsman topology on function spaces
zbMATH Open document ID: 0874.54012
DOI: 10.1007/BF02844473
author: Giuseppe Di Maio
author: Ľubica Holá
publication date: 1997-11-09T00:00:00Z
review text: Let \(X\) and \(Y\) be metric spaces and let \(X\times Y\) be assigned the product box metric. Let each continuous function on \(X\) to \(Y\) be identified with its graph, a subset of \(X\times Y\). The authors study on the space of continuous functions, the topology induced on their graphs, by the Wijsman hyperspace topology on \(\text{CL} (X\times Y)\). Earlier, the reviewer had studied a similar topology in the context of uniform spaces [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 18, 343-358 (1988; Zbl 0649.54008)]. Authors compare the two topologies, giving conditions when they coincide and give examples to show their differences. They also compare their topology with other well-known topologies. The paper is well written and contains several interesting results.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 1036017
zbMATH Keywords: compact-open
zbMATH Keywords: pointwise convergence
zbMATH Keywords: Wijsman hyperspace topology
reviewed by: S. Naimpally
MaRDI profile type: Publication
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published in: Rendiconti del Circolo Matematico di Palermo
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description: scientific article; zbMATH DE number 1036017