Inscribing closed non-$\sigma$-lower porous sets into Suslin non-$\sigma$-lower porous sets

Abstract

The main aim of this paper is to prove that every non-$\sigma$-lower porous Suslin set in a topologically complete metric space contains a closed non-$\sigma$-lower porous subset. In fact, we prove a general result of this type on “abstract porosities.” This general theorem is also applied to ball small sets in Hilbert spaces and to $\sigma$-cone-supported sets in separable Banach spaces.