On O'Malley lower porouscontinuous functions (Q6629721)

The authors introduce and study the concept of \textit{lower porous continuity in the sense of O'Malley} of a function \(f\colon\mathbb{R}\to\mathbb{R}\). These ideas arise from the definition of \textit{ porous continuity}, which was defined by \textit{J. Borsík} and \textit{J. Holos}, [Math. Slovaca 64, No. 3, 741--750 (2014; Zbl 1340.54028)], and \textit{ porous continuity in the sense of O'Malley}, see \textit{I. Domnik} et al., [Tatra Mt. Math. Publ. 78, 9--24 (2021; Zbl 1483.54008)]. The main difference is that the upper porosity is replaced by the lower porosity in these definitions.