Wijsman topology on function spaces
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.
scientific article; zbMATH DE number 1036017
scientific article