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2015 Analogues of Transitiveness and Decomposition of Continuity
Nesterenko Vasyl’, Maslyuchenko Volodymyr
Real Anal. Exchange 40(2): 355-370 (2015).


We consider two conditions that weaken the closed graph condition and we study their properties. We show that if $X$ is a locally connected Baire space, $Y$ is a separable metrizable space and $f:X \to Y$ is a $w^*$-quasi-continuous, almost continuous and weakly Darboux function, then $f$ is continuous.


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Nesterenko Vasyl’. Maslyuchenko Volodymyr. "Analogues of Transitiveness and Decomposition of Continuity." Real Anal. Exchange 40 (2) 355 - 370, 2015.


Published: 2015
First available in Project Euclid: 4 April 2017

zbMATH: 06848840
MathSciNet: MR3499769

Primary: 26A15 , ‎54C30

Keywords: almost continuity , closed graph , Darboux properties , decomposition of continuity , locally $w^*$-continuous , locally relative continuous , transitional mapping

Rights: Copyright © 2015 Michigan State University Press

Vol.40 • No. 2 • 2015
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