Real Analysis Exchange

Quasi-Continuity of Horizontally Quasi-Continuous Functions

Alireza Kamel Mirmostafaee

Abstract

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

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

Dates
First available in Project Euclid: 30 June 2015

https://projecteuclid.org/euclid.rae/1435669999

Mathematical Reviews number (MathSciNet)
MR3365378

Zentralblatt MATH identifier
1322.54009

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

Citation

Kamel Mirmostafaee, Alireza. Quasi-Continuity of Horizontally Quasi-Continuous Functions. Real Anal. Exchange 39 (2014), no. 2, 335--344. https://projecteuclid.org/euclid.rae/1435669999