On Metric Boundedness Structures

Set-Valued Analysis

Volumn 7, Issue 3, 1999, Pages 195-208

  Beer, Gerald ^a  

^a CALIFORNIA STATE UNIVERSITY   (United States)

Author keywords

Attouch Wets topology; Bornology; Bounded set; Convergence to infinity; Hyperspace; Metric space; UC space; Uniformly equivalent metrics; Wijsman topology

Indexed keywords

EID: 0038923428     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008720619545     Document Type: Article

References (20)

1. Atsuji, M.: Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 11-16.
2. Beer, G.: The slice topology: A viable alternative to Mosco convergence in nonreflexive spaces, Nonlinear Anal. 19 (1992), 271-290.
3. Beer, G.: Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, Dordrecht, Holland, 1993.
4. Beer, G.: Quasi-concave functions and convex convergence to infinity, to appear in Bull. Austral. Math. Soc.
5. Beer, G. and DiConcilio, A.: Uniform continuity on bounded sets and the Attouch-Wets topology, Proc. Amer. Math. Soc. 112 (1991), 235-243.
6. Beer, G., Lechicki, A., Levi, S. and Naimpally, S.: Distance functional and suprema of hyperspace topologies, Ann. Mat. Pura Appl. 162 (1992), 367-381.
7. Beer, G. and Tamaki, R.: On hit-and-miss hyperspace topologies, Comment. Math. Univ. Carolinae 34 (1993), 717-728.
8. Bing, R. H.: Extending a metric, Duke Math. J. 14 (1947), 511-519.
9. Blumenthal, L.: Theory and Applications of Distance Geometry, Clarendon Press, Oxford, 1953.
10. Cornet, B.: Topologies sur les fermés d'un espace métrique, Cahiers de mathématiques de la décision 7309, Université de Paris, Dauphine, 1973.
11. Costantini, C., Levi, S. and Zieminska, J.: Metrics that generate the same hyperspace convergence, Set-Valued Anal. 1 (1993), 141-158.
12. Engelking, R.: General Topology, Polish Scientific Publishers, Warsaw, 1977.
13. Francaviglia, S., Lechicki, A. and Levi, S.: Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions, J. Math. Anal. Appl. 112 (1985), 347-370.
14. Hess, C.: Contributions à l'étude de la mesurabilité, de la loi de probabilité, et de la convergence des multifunctions, Thèse d'état, Université Montpellier II, 1986.
15. Hogbe-Nlend, H.: Bornologies and Functional Analysis, Math. Stud. 26, North-Holland, Amsterdam, 1977.
16. Holmes, R.: Geometric Functional Analysis, Springer-Verlag, New York, 1975.
17. Hu, S.-T.: Boundedness in a topological space, J. Math. Pures Appl. 28 (1949), 287-320.
18. Hu, S.-T.: Introduction to General Topology, Holden-Day, San Francisco, 1966.
19. Rainwater, J.: Spaces whose finest uniformity is metric, Pacific J. Math. 9 (1959), 567-570.
20. Toader, Gh.: On a problem of Nagata, Mathematica (Cluj) 20 (1978), 78-79.