Real Analysis Exchange

Quasi-Continuity of Horizontally Quasi-Continuous Functions

Alireza Kamel Mirmostafaee

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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.

Article information

Real Anal. Exchange, Volume 39, Number 2 (2014), 335-344.

First available in Project Euclid: 30 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 54C08: Weak and generalized continuity 54C05: Continuous maps
Secondary: 54E52: Baire category, Baire spaces

Quasi-continuity Horizontally quasi-continuous functions Topological games


Kamel Mirmostafaee, Alireza. Quasi-Continuity of Horizontally Quasi-Continuous Functions. Real Anal. Exchange 39 (2014), no. 2, 335--344.

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