On Small Subsets of the Space of Darboux Functions
Joanna Kucner, Ryszard J. Pawlak, and Bożena Świątek
Source: Real Anal. Exchange Volume 25, Number 1
(1999), 343-358.
Abstract
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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Permanent link to this document: http://projecteuclid.org/euclid.rae/1231187608
Mathematical Reviews number (MathSciNet): MR1758010
Zentralblatt MATH identifier: 1015.26008
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