Geodesic
Topologies Associated with Kuratowski-Painlevé Convergence of Closed Sets
Journal of convex analysis, Tome 17 (2010) no. 3, pp. 805-826.

Voir la notice de l'article provenant de la source Heldermann Verlag

The main purpose of this paper is to identify topologies on the closed subsets C(X) of a Hausdorff space X that are sequentially equivalent to classical Kuratowski-Painlevé convergence K. This reduces to a study of upper topologies sequentially equivalent to upper Kuratowski-Painlevé convergence K+, where we are of course led to consider the sequential modification of upper Kuratowski-Painlevé convergence. We characterize those miss topologies induced by a cobase of closed sets that are sequentially equivalent to K+, with special attention given to X first countable. Separately in the final section, we revisit Mrowka's theorem on the compactness of Kuratowski-Painlevé convergence.
Classification : 54B20, 54A20, 54E35
Mots-clés : Fell topology, Kuratowski-Painleve convergence, hyperspace, hit-and-miss topology, modification, sequential modification, subsequential selector 
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     author = {G. Beer and J. Rodr{\'\i}guez-L\'opez},
     title = {Topologies {Associated} with {Kuratowski-Painlev\'e} {Convergence} of {Closed} {Sets}},
     journal = {Journal of convex analysis},
     pages = {805--826},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a7/}
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G. Beer; J. Rodríguez-López. Topologies Associated with Kuratowski-Painlevé Convergence of Closed Sets. Journal of convex analysis, Tome 17 (2010) no. 3, pp. 805-826. http://geodesic.mathdoc.fr/item/JCA_2010_17_3_JCA_2010_17_3_a7/