arXiv subjects
Publications and source records attributed to Andrzej Nowik.
We investigate the $σ$-porosity of certain known ideals of subsets of natural numbers. Porosity is a notion of smallness in metric spaces that is stronger than nowhere density. Analogously, $σ$-porosity is a strengthening of meagerness. In this paper, we verify which ideals are $σ$-porous.
The paper contains two results pointing to the lack of symmetry between measure and category. Assume CH. There exists a strongly meager subset of the Cantor set that can be mapped onto the Cantor set by a uniformly continuous function. (It is well known that uniformly continuous image of a strongly null set is strongly null). A ZFC version of this result is also given.