Further characterizations of boundedly UC spaces

Ľubica Holá; Dušan Holý

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 1, page 175-183
  • ISSN: 0010-2628

Abstract

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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 UC spaces are given.

How to cite

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Holá, Ľubica, and Holý, Dušan. "Further characterizations of boundedly UC spaces." Commentationes Mathematicae Universitatis Carolinae 34.1 (1993): 175-183. <http://eudml.org/doc/247483>.

@article{Holá1993,
abstract = {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.},
author = {Holá, Ľubica, Holý, Dušan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$\operatorname\{UC\}$ space; boundedly $\operatorname\{UC\}$ space; boundedly compact space; compact-open topology; topology of uniform convergence on bounded sets; Attouch-Wets topology; bounded proximal topology; boundedly UC space; Attouch-Wets topology; hyperspace topologies},
language = {eng},
number = {1},
pages = {175-183},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Further characterizations of boundedly UC spaces},
url = {http://eudml.org/doc/247483},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Holá, Ľubica
AU - Holý, Dušan
TI - Further characterizations of boundedly UC spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 1
SP - 175
EP - 183
AB - 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.
LA - eng
KW - $\operatorname{UC}$ space; boundedly $\operatorname{UC}$ space; boundedly compact space; compact-open topology; topology of uniform convergence on bounded sets; Attouch-Wets topology; bounded proximal topology; boundedly UC space; Attouch-Wets topology; hyperspace topologies
UR - http://eudml.org/doc/247483
ER -

References

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  2. Attouch H., Wets R., Quantitative stability of variational systems I, The epigraphical distances, preprint. MR1018570
  3. Attouch H., Lucchetti R., Wets R., The topology of the ρ -Hausdorff distance, to appear in Annali Mat. Pure Appl. Zbl0769.54009
  4. Aze D., Penot J., Operations on convergent families of sets and functions, Optimization 21 (1990), 521-534. (1990) Zbl0719.49013MR1069660
  5. Beer G., Metric spaces on which continuous functions are uniformly continuous and Hausdorff distance, Proc. Amer. Math. Soc. 95 (1985), 653-658. (1985) Zbl0594.54007MR0810180
  6. Beer G., DiConcilio A., A generalization of boundedly compact metric spaces, Comment. Math. Univ. Carolinae 32 (1991), 362-367. (1991) MR1137797
  7. Beer G., DiConcilio A., Uniform continuity on bounded sets and the Attouch-Wets topology, Proc. Amer. Math. Soc. 112 (1991), 235-244. (1991) MR1033956
  8. Beer G., Lucchetti R., Weak topologies for the closed subsets of a metrizable space, to appear in Trans. Amer. Math. Soc. Zbl0810.54011MR1094552
  9. Beer G., Lucchetti R., Well-posed optimization problems and a new topology for the closed subsets of a metric space, preprint. Zbl0812.54015MR1256444
  10. Beer G., Lechicki A., Levi S., Naimpally S., Distance functionals and the suprema of hyperspace topologies, to appear in Annali Mat. Pure Appl. 
  11. Holá Ł., The Attouch-Wets topology and a characterization of normable linear spaces, Bull. Austral. Math. Soc. 44 (1991), 11-18. (1991) MR1120389
  12. Lechicki A., Levi S., Wijsman convergence in the hyperspace of a metric space, Bull. Un. Mat. Ital. 5-B (1987), 435-452. (1987) Zbl0655.54007MR0896334
  13. Penot J.P., The cosmic Hausdorff topology, the bounded Hausdorff topology, and continuity of polarity, to appear in Proc. Amer. Math. Soc. Zbl0774.54008MR1068129

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