Open Access
2013/2014 Quasi-Continuity of Horizontally Quasi-Continuous Functions
Alireza Kamel Mirmostafaee
Real Anal. Exchange 39(2): 335-344 (2013/2014).


Let \(X\) be a Baire space, \(Y\) a topological space, \(Z\) a regular space and \(f:X \times Y \to Z\) be a horizontally quasi-continuous function. We will show that if \(Y\) is first countable and \(f\) is quasi-continuous with respect to the first variable, then every horizontally quasi-continuous function \(f:X \times Y \to Z\) is jointly quasi-continuous. This will extend Martin’s Theorem of quasi-continuity of separately quasi-continuous functions for non-metrizable range. Moreover, we will prove quasi-continuity of \(f\) for the case \(Y\) is not necessarily first countable.


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Alireza Kamel Mirmostafaee. "Quasi-Continuity of Horizontally Quasi-Continuous Functions." Real Anal. Exchange 39 (2) 335 - 344, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 30 June 2015

zbMATH: 1322.54009
MathSciNet: MR3365378

Primary: 54C05 , 54C08
Secondary: 54E52

Keywords: Horizontally quasi-continuous functions , quasi-continuity , ‎topological games

Rights: Copyright © 2014 Michigan State University Press

Vol.39 • No. 2 • 2013/2014
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