On O’malley Lower Porouscontinuous Functions

In 2014, J. Borsík and J. Holos defined porouscontinuous functions. Using the notion of density in the sense of O’Malley, new definitions of porouscontinuity were introduced in 2021, namely ℳ𝒪_r and 𝒮𝒪_r-continuity. These kinds of porouscontinuity used upper porosity. We consider lower porous-continuity in the sense of O’Malley, where lower porosity is used instead of standard (upper) porosity.