Abstract
Let $f\colon \mathbb R\to\mathbb R$ and let $D_f$ denote the set of points of discontinuity of $f$. First it is proved that if $f|_{D_f}$ is continuous, then $D$ is a nowhere dense, $F_\sigma$ set. The major result is that if $D$ is a nowhere dense, $F_\sigma$ set then there is a function $f$ such that $D_f=D$ and $f|_D$ is continuous. Finally it is shown that such functions are of Baire class one.
Citation
William J. Gorman. Clifford E. Weil. "Functions Continuous Relative to Their Sets of Discontinuity." Real Anal. Exchange 49 (1) 235 - 240, 2024. https://doi.org/10.14321/realanalexch.49.1.1686207848
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