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On monotone minimal cuscos

Karel Pastor, Dušan Bednařík (2001)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On multifunctions with closed graphs

D. Holý (2001)

Mathematica Bohemica

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.

On multifunctions with convex graph

Biagio Ricceri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

On reflexive closed set lattices

Zhongqiang Yang, Dong Sheng Zhao (2010)

Commentationes Mathematicae Universitatis Carolinae

For a topological space X , let S ( X ) denote the set of all closed subsets in X , and let C ( X ) denote the set of all continuous maps f : X X . A family 𝒜 S ( X ) is called reflexive if there exists 𝒞 C ( X ) such that 𝒜 = { A S ( X ) : f ( A ) A for every f 𝒞 } . Every reflexive family of closed sets in space X forms a sub complete lattice of the lattice of all closed sets in X . 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...

On selections of multifunctions

Milan Matejdes (1993)

Mathematica Bohemica

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.

On semigroups with an infinitesimal operator

Jolanta Olko (2005)

Annales Polonici Mathematici

Let F t : t 0 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 F t is invertible and there exists an exponential semigroup f t : t 0 of linear continuous selections f t of F t .

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