Resolvability of abstract density topologies in $\mathbb{R}^n$ generated by lower or almost lower density operators

Abstract

Maximal resolvability and extraresolvability(with $\operatorname {MA}$) of abstract
density topologies in $\mathbb{R}^n$ generated by lower or almost lower density operators is shown. We note that in some models of $\operatorname {ZFC}$ the abstract density topologies in $\mathbb{R}^n$ generated by a lower density operator can be not extraresolvable.