On O'Malley lower porouscontinuous functions

Abstract

In 2014 J. Bors\'{i}k and J. Holos defined porouscontinuous functions. Using the notion of density in the sense of O'Malley in 2021 new definitions of porouscontinuity were introduced, namely $\mathcal{MO}_r$ and $\mathcal{SO}_r$-continuity. These kinds of porouscontinuity used upper porosity. We consider lower porouscontinuity in the sense of O'Malley, where lower porosity is used instead of standard (upper) porosity.