Characterization of quasi-continuity of multifunctions of two variables
type: Item
instance of: scholarly article
title: Characterization of quasi-continuity of multifunctions of two variables
zbMATH Open document ID: 1389.54054
author: Olena Fotiy
author: O. V. Maslyuchenko
author: V. V. Nesterenko
published in: Mathematica Slovaca
publication date: 2016-06-07T00:00:00Z
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 6589832
zbMATH Keywords: multifunction
zbMATH Keywords: upper quasi-continuity
zbMATH Keywords: lower quasi-continuity
zbMATH Keywords: symmetrically upper quasi-continuity
zbMATH Keywords: symmetrically lower quasi-continuity
zbMATH Keywords: upper horizontally quasi-continuity
zbMATH Keywords: lower horizontally quasi-continuity
MaRDI profile type: Publication
full work available at URL: ms-2015-0135
OpenAlex ID: W2345691984
DOI: 10.1515/MS-2015-0135
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review text: The authors investigate the relationship between separate and joint quasi-continuity of a multifunction with two variables, continuing the previous work of \textit{S. Kempisty} [Fundam. Math. 19, 184--197 (1932; Zbl 0005.19802)] and [\textit{T. Neubrunn}, Math. Slovaca 32, 147--154 (1982; Zbl 0483.54009)]. The main result of this paper is a theorem stating the necessary and sufficient conditions for a multifunction with two variables to be jointly quasi-continuous. It says that a compact-valued multifunction \(F\: X \times Y \rightarrow Z\), where \(X\) is a Baire space, \(Y\) is a second countable space and \(Z\) is a separable metrizable space, is quasi-continuous if and only if \(F\) is horizontally quasi-continuous and there exists a residual subset \(M\) of \(X\) such that for any \(x \in M\) the multifunction \(F^x = F(x, \cdot)\) is quasi-continuous on \(Y\).
description: scientific article; zbMATH DE number 6589832