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2004-2005 Separately Continuous Functions with Closed Graphs
Michal Ryszard Wojcik, Michal Stanislaw Wojcik
Real Anal. Exchange 30(1): 23-28 (2004-2005).


In this paper we prove that if $f:\R\times\R\to\R$ has a closed graph and all of its $x$-sections are continuous, and at least one $y$-section is continuous, then $f$ is continuous. It was already proved by Piotrowski and Wingler [PW] that if $f:\R\times\R\to\R$ has a closed graph and is separately continuous, then $f$ is continuous. Our result is stronger.


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Michal Ryszard Wojcik. Michal Stanislaw Wojcik. "Separately Continuous Functions with Closed Graphs." Real Anal. Exchange 30 (1) 23 - 28, 2004-2005.


Published: 2004-2005
First available in Project Euclid: 27 July 2005

zbMATH: 1064.54020
MathSciNet: MR2126791

Primary: 54C05

Keywords: closed graph , continuity , separate continuity

Rights: Copyright © 2004 Michigan State University Press

Vol.30 • No. 1 • 2004-2005
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