Following the paper [BDC1], further relations between the classical topologies on function spaces and new ones induced by hyperspace topologies on graphs of functions are introduced and further characterizations of boundedly $\operatorname{UC}$ spaces are given.
@article{118567, author = {\v Lubica Hol\'a and Du\v san Hol\'y}, title = {Further characterizations of boundedly UC spaces}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {175-183}, zbl = {0828.54016}, mrnumber = {1240215}, language = {en}, url = {http://dml.mathdoc.fr/item/118567} }
Holá, Ľubica; Holý, Dušan. Further characterizations of boundedly UC spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 175-183. http://gdmltest.u-ga.fr/item/118567/
Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 11-16. (1958) | MR 0099023 | Zbl 0082.16207
Quantitative stability of variational systems I, The epigraphical distances, preprint. | MR 1018570
The topology of the $\rho $-Hausdorff distance, to appear in Annali Mat. Pure Appl. | Zbl 0769.54009
Operations on convergent families of sets and functions, Optimization 21 (1990), 521-534. (1990) | MR 1069660 | Zbl 0719.49013
Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance, Proc. Amer. Math. Soc. 95 (1985), 653-658. (1985) | MR 0810180 | Zbl 0594.54007
A generalization of boundedly compact metric spaces, Comment. Math. Univ. Carolinae 32 (1991), 362-367. (1991) | MR 1137797
Uniform continuity on bounded sets and the Attouch-Wets topology, Proc. Amer. Math. Soc. 112 (1991), 235-244. (1991) | MR 1033956
Weak topologies for the closed subsets of a metrizable space, to appear in Trans. Amer. Math. Soc. | MR 1094552 | Zbl 0810.54011
Well-posed optimization problems and a new topology for the closed subsets of a metric space, preprint. | MR 1256444 | Zbl 0812.54015
Distance functionals and the suprema of hyperspace topologies, to appear in Annali Mat. Pure Appl.
The Attouch-Wets topology and a characterization of normable linear spaces, Bull. Austral. Math. Soc. 44 (1991), 11-18. (1991) | MR 1120389
Wijsman convergence in the hyperspace of a metric space, Bull. Un. Mat. Ital. 5-B (1987), 435-452. (1987) | MR 0896334 | Zbl 0655.54007
The cosmic Hausdorff topology, the bounded Hausdorff topology, and continuity of polarity, to appear in Proc. Amer. Math. Soc. | MR 1068129 | Zbl 0774.54008