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1999/2000 On Small Subsets of the Space of Darboux Functions
Joanna Kucner, Ryszard J. Pawlak, Bożena Świątek
Real Anal. Exchange 25(1): 343-358 (1999/2000).


We prove that the set $\cal{F}$ of all bounded functionally connected functions is boundary in the space of all bounded Darboux functions (with the metric of uniform convergence). Next we prove that the set of bounded upper (lower)semi-continuous Darboux functions and the set of all bounded quasi-continuous functionally connected functions is porous at each point of the space $\cal{F}$.


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Joanna Kucner. Ryszard J. Pawlak. Bożena Świątek. "On Small Subsets of the Space of Darboux Functions." Real Anal. Exchange 25 (1) 343 - 358, 1999/2000.


Published: 1999/2000
First available in Project Euclid: 5 January 2009

zbMATH: 1015.26008
MathSciNet: MR1758010

Primary: 26A21 , 26A24

Keywords: Darboux function , functionally connected function , porosity , quasi-continuous function

Rights: Copyright © 1999 Michigan State University Press

Vol.25 • No. 1 • 1999/2000
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