Ideals of porous sets in the real line and in metrizable topological spaces

Abstract

Porous sets and spherically porous sets of a metric space are studied. In particular, porous, superporous, and equiporous sets of a metric space (X, π) are characterized from the topological point of view. Metrizable spaces that are spherically porous in themselves with respect to some metric generating the topology are characterized. Some relations between the ideals of the classes of porous sets in the real line are established. Bibliography: 13 titles.