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Čech-completeness and related properties of the generalized compact-open topology

Holá L`., Zsilinszky L.

Journal of Applied Analysis

2010

Vol. 16, nr 1

151-169

The generalized compact-open topology τc on partial continuous functions with closed domains in X and values in Y is studied. If Y is a non-countably compact Čech-complete space with a Gδ-diagonal, then τc is Čech-complete, sieve complete and satisfies the p-space property of Arhangel'skii, respectively, if and only if X is Lindelof and locally compact. Lindelofness, paracompactness and normality of τc is also investigated. New results are obtained on Čech-completeness, sieve completeness and the p-space property for the compact-open topology on the space of continuous functions with a general range Y.

The spaces of closed convex sets in Euclidean spaces with the fell topology

Sakai K., Yang Z.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

Vol. 55, no 2

139-143

Let ConvF(Rn) be the space of all non-empty closed convex sets in Euclidean space Rn endowed with the Fell topology. We prove that ConvF(lRn) ≈ Rn x Q for every n > 1 whereas ConvF(R) ≈ R x I.

Uniform structures on hyperspaces and uniform topologies on spaces of multifunctions

Del Prete I., Di Iorio M., Holá Ľ.

Demonstratio Mathematica

2003

Vol. 36, nr 4

985--1000

The aim of this paper is to study uniform and topological structures on spaces of multifunctions. Uniform structures on hyperspaces compatible with the Fell, the Wijsman and the Hausdorff metric topology respectively are studied and the links between them are explored. Topologies induced by the above uniformities on spaces of multifunctions are considered and compared. Also connections between uniform convergence of multifunctions and their equi-semicontinuity are investigated.