On the strong quasi-continuity of multivalued maps of two variables (Q2774497)
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scientific article; zbMATH DE number 1713808
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the strong quasi-continuity of multivalued maps of two variables |
scientific article; zbMATH DE number 1713808 |
Statements
28 February 2002
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multifunctions
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strong quasi-continuity
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density topology
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cliquishness
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On the strong quasi-continuity of multivalued maps of two variables (English)
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The paper deals with enlargement of known results concerning strong quasi-continuity and cliquishness of real functions of two variables for multivalued maps. It is known [see \textit{T. Neubrunn}, Real Anal. Exch. 14, No. 2, 259-306 (1989; Zbl 0679.26003)] that the upper (lower) quasi-continuity of \(x\)-sections of \(F\) and both upper and lower quasi-continuity of \(y\)-sections of \(F\) imply the upper (lower) quasi-continuity of \textit{M. Matejdes} [Real Anal. Exch. 18, No. 1, 214-220 (1993; Zbl 0782.54019)] which gives a generalization of a result of Fudali about cliquishness on multivalued map. The situation is different for strong cliquishness and quasi-continuity investigated by \textit{Z. Grande} [Real Anal. Exch. 21 No. 1, 236-243 (1996; Zbl 0851.26005)]. NEWLINENEWLINENEWLINEThe author modifies the notions of \(H(x,y)\) and \(K(x,y)\) introduced by \textit{Z. Grande} [loc. cit.] to the case of multivalued maps and gives some generalizations of his results.
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