Abstract
A cliquish function $f: \mathbb R\to\mathbb R$ is internally cliquish if its set of discontinuity points is nowhere dense. A Baire $1$ function $f: \mathbb R\to\mathbb R$ is internally Baire $1$ if its set of discontinuity points is nowhere dense. In this paper we proved that the set of Darboux internally cliquish (Baire $1$) functions is dense and $\sigma$-strongly porous in the family of Darboux cliquish (Baire $1$) functions.
Citation
Gertruda Ivanova. Irena Domnik. "On Density and Sigma-Porosity in Some Families of Darboux Functions." Real Anal. Exchange 47 (1) 63 - 74, 2022. https://doi.org/10.14321/realanalexch.47.1.1590599512
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