Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T00:09:39.877Z Has data issue: false hasContentIssue false

A Topology for the Solid Subsets of a Topological Space

Published online by Cambridge University Press:  20 November 2018

Roberto Lucchetti
Affiliation:
Department of Mathematics via Saldini 50 20133 Milano Italy
Anna Torre
Affiliation:
Department of Mathematics Strada Nuova 65 Pavia Italy
Roger J.-B. Wets
Affiliation:
Department of Mathematics University of California Davis, California 95616 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A new topology for the closed subsets of a topological space X which are the closure of their interiors is defined and investigated. Some applications to convergence of regular measures are also given.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

[AF] Aubin, J-R and Frankowska, H., Set valued analysis, Birkauser, Boston, 1990.Google Scholar
[ALAttouch, W. H., Lucchetti, R. and R. J.-Wets, B., The topology of the p-Hausdorff distance, Annali Mat. Pura e Appl., Série IV, 160(1992), 303320.Google Scholar
[Bel] Beer, G., Metric spaces with nice closed balls and distance functions for closed sets, Bull Australian Math. Soc, (1987), 81-96.Google Scholar
[Be2], An embedding theorem for the Fell topology, Michigan Math. J. 35(1988), 39.Google Scholar
[BLLN] Beer, G., Lechicki, A., Levi, S. and Naimpally, S., Distance junctionals the suprema of hyperspace topologies, Annali Mat. Pura e Appl., Série IV, 162(1992), 367381.Google Scholar
[BL1] Beer, G. and Lucchetti, R., Convex optimization and the epi-distance topology, Trans. Amer. Math. Soc. 327(1991), 795814.Google Scholar
[BL2], Weak topologies for the closed subsets of a metrizable space, Trans. Amer. Math. Soc, to appear.Google Scholar
[BT] P.Billingsley and Topsoe, F., Uniformity in weak convergence, Z. fur Wahrscheinlichkeitstheorie und verwandte Gebiete 7(1967), 116.Google Scholar
[Ch] Chichilniski, G., Spaces of economic agents, J. of Economic Theory 15(1977), 160173.Google Scholar
[En] Engelking, R., General Topology, Polish Scientific Publishers, Warsaw, 1977.Google Scholar
[FLL] Francaviglia, S., Lechicki, A. and Levi, S., Quasi-uniformization of hyperspaces and convergence of nets of semicontinuous multifunctions, J. Math. Anal. Appl. 112(1985), 347370.Google Scholar
[GH] Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. and Scott, D. S., A compendium of continuous lattices, Springer Verlag, New York, 1980.Google Scholar
[KKhan, S. A. and Sun, Y., On complete regularity of spaces of economic agents endowed with the order topology, Archiv der Mathematic 54(1990), 389396.Google Scholar
[KT] Klein, E. and Thompson, A., Theory of correspondences, Wiley, New York, 1984.Google Scholar
[Ku] Kuratowski, K., Topology, Academic Press, New York, 1966.Google Scholar
[Lu] Lucchetti, R., Ph.Dissertation, D., University of California at Davis, 1989.Google Scholar
[LSW] Lucchetti, R., Salinetti, G. and R. J-Wets, B., Uniform convergence of probability measures: topological criteria, to appear.Google Scholar
[LT] Lucchetti, R. and Torre, A., Hyperspace topologies, in preparation.Google Scholar
[Mi] Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71(1951), 152182 [Se] L. Schwartz, Radon spaces, Oxford University Press, 1977.Google Scholar
[SW]Salinetti, W. G. and Wets, R. J.-B., A Glivenko-Cantelli type theorem: an application of the convergence theory of stochastic suprema, Annals of Oper. Res., (1991), to appear.Google Scholar