A Topology for the Solid Subsets of a Topological Space
Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 197-208

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1993-029-5
Mots-clés : 54B20, hyperspace topologies, solid sets, narrow convergence of probability measures
Lucchetti, Roberto; Torre, Anna; Wets, Roger J.-B. A Topology for the Solid Subsets of a Topological Space. Canadian mathematical bulletin, Tome 36 (1993) no. 2, pp. 197-208. doi: 10.4153/CMB-1993-029-5
@article{10_4153_CMB_1993_029_5,
     author = {Lucchetti, Roberto and Torre, Anna and Wets, Roger J.-B.},
     title = {A {Topology} for the {Solid} {Subsets} of a {Topological} {Space}},
     journal = {Canadian mathematical bulletin},
     pages = {197--208},
     year = {1993},
     volume = {36},
     number = {2},
     doi = {10.4153/CMB-1993-029-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-029-5/}
}
TY  - JOUR
AU  - Lucchetti, Roberto
AU  - Torre, Anna
AU  - Wets, Roger J.-B.
TI  - A Topology for the Solid Subsets of a Topological Space
JO  - Canadian mathematical bulletin
PY  - 1993
SP  - 197
EP  - 208
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-029-5/
DO  - 10.4153/CMB-1993-029-5
ID  - 10_4153_CMB_1993_029_5
ER  - 
%0 Journal Article
%A Lucchetti, Roberto
%A Torre, Anna
%A Wets, Roger J.-B.
%T A Topology for the Solid Subsets of a Topological Space
%J Canadian mathematical bulletin
%D 1993
%P 197-208
%V 36
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-029-5/
%R 10.4153/CMB-1993-029-5
%F 10_4153_CMB_1993_029_5

[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), 303–320. Google Scholar

Beer, G., Metric spaces with nice closed balls and distance functions for closed sets, Bull Australian Math. Soc, (1987), 81-96. Google Scholar

, An embedding theorem for the Fell topology, Michigan Math. J. 35(1988), 3–9. 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), 367–381. Google Scholar

Beer, G. and Lucchetti, R., Convex optimization and the epi-distance topology, Trans. Amer. Math. Soc. 327(1991), 795–814. Google Scholar

, Weak topologies for the closed subsets of a metrizable space, Trans. Amer. Math. Soc, to appear. Google Scholar

Billingsley and Topsoe, F., Uniformity in weak convergence, Z. fur Wahrscheinlichkeitstheorie und verwandte Gebiete 7(1967), 1–16. Google Scholar

[Ch] Chichilniski, G., Spaces of economic agents, J. of Economic Theory 15(1977), 160–173. Google Scholar

Engelking, R., General Topology, Polish Scientific Publishers, Warsaw, 1977. Google Scholar

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. Google Scholar

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), 389–396. Google Scholar

Klein, E. and Thompson, A., Theory of correspondences, Wiley, New York, 1984. Google Scholar

Kuratowski, K., Topology, Academic Press, New York, 1966. Google Scholar

Lucchetti, R., Ph.Dissertation, D., University of California at Davis, 1989. Google Scholar

Lucchetti, R., Salinetti, G. and R. J-Wets, B., Uniform convergence of probability measures: topological criteria, to appear. Google Scholar

Lucchetti, R. and Torre, A., Hyperspace topologies, in preparation. Google Scholar

Michael, E., Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71(1951), 152–182 [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

Cité par Sources :