Abstract

The main purpose of this paper is to identify topologies on the closed subsets C(X)\mathscr{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.

Author information

Contact details are reproduced from the original publication and may be historical.

Gerald Beer

Dept. of Mathematics, California State University, 5151 State University Drive, Los Angeles, CA 90032, U.S.A.

gbeer@cslanet.calstatela.edu

Jesús Rodríguez-López

Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica, 46022 Valencia, Spain

jrlopez@mat.upv.es

Keywords

  • Fell topology
  • Kuratowski-Painlevé convergence
  • hyperspace
  • hit-and-miss topology
  • modification
  • sequential modification
  • subsequential selector

Mathematics Subject Classification

54B20; 54A20, 54E35

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Suggested citation

G. Beer, J. Rodríguez-López. “Topologies Associated with Kuratowski-Painlevé Convergence of Closed Sets.” Journal of Convex Analysis 17 (2010), No. 3&4, 805–826. https://doi.org/10.68381/jca17053

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