On Extensions of Multivalued Mappings of Topological Spaces
The set of points of upper semicontinuity of multi-valued mappings with a closed graph is studied. A topology on the space of multi-valued mappings with a closed graph is introduced.
In questa Nota viene stabilita una caratterizzazione generale della semicontinuità inferiore delle multifunzioni, a grafico convesso, definite in sottoinsieme non vuoto, aperto e convesso di uno spazio vettoriale topologico e a valori in uno spazio vettoriale topologico localmente convesso. Sono poste in luce, poi, varie conseguenze di tale caratterizzazione.
For a topological space , let denote the set of all closed subsets in , and let denote the set of all continuous maps . A family is called reflexive if there exists such that for every . Every reflexive family of closed sets in space forms a sub complete lattice of the lattice of all closed sets in . In this paper, we continue to study the reflexive families of closed sets in various types of topological spaces. More necessary and sufficient conditions for certain families of closed...
The purpose of this paper is to introduce a definition of cliquishness for multifunctions and to study the search for cliquish, quasi-continuous and Baire measurable selections of compact valued multifunctions. A correction as well as a generalization of the results of [5] are given.
Let be an iteration semigroup of linear continuous set-valued functions. If the semigroup has an infinitesimal operator then it is a uniformly continuous semigroup majorized by an exponential semigroup. Moreover, for sufficiently small t every linear selection of is invertible and there exists an exponential semigroup of linear continuous selections of .