On Small Subsets of the Space of Darboux Functions

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 $\cal{F}$.