Inscribing closed non-σ-lower porous sets into Suslin non-σ-lower porous sets

Abstract

The main aim of this paper is to prove that every non-σ-lower porous Suslin set in a topologically complete metric space contains a closed non-σ-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 σ-cone-supported sets in separable Banach spaces.