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On continuous convergence of nets of multifunctions

Przemski M.

Demonstratio Mathematica

2011

Vol. 44, nr 1

181--200

This paper expands the classical concept of the continuous convergence of nets of multifunctions introduced by Cao, Reilly and Vamanamurthy in [7]. We introduce some new types of properties of convergence of such nets which guarantee the upper or lower semicontinuity of the limit multifunction. Furthermore, we obtain some analogous results concerning generalized continuity properties of multifunctions.

On single-valued and multi-valued convergences

Bacher Ł., Kamiński A., Nalepa R.

Journal of Mathematics and Applications

2009

Vol. 31

19-27

We present a review of ideas of a general theory of convergence, developed independently of topology, with the stress on the duality of convergence and topology. Results and problems concerning sufficient and necessary conditions for a convergence to be topological, both in case of the single- and multi-valued cases, are recalled. We reconstruct, filling certain gaps, an example given in [7] to show that one of sufficient conditions in the theorems proved in [1] and [9] for multi-valued convergences to be topological is not necessary.