Porosity in Spaces of Darboux-Like Functions

Abstract

It is known that the six Darboux-like function spaces of continuous, extendable, almost continuous, connectivity, Darboux, and peripherally continuous functions $f\:R\to \R$, with the metric of uniform convergence, form a strictly increasing chain of subspaces. We denote these spaces by \C, \E, \AC, \Conn, \D, and \PC, respectively. We show that C and D are porous and AC and Conn are not porous in their successive spaces of this chain.