Products of non-σ-lower porous sets

Abstract

In the present article we provide an example of two closed non-σ-lower porous sets A,B ⊆ ℝ such that the product A × B is lower porous. On the other hand, we prove the following: Let X and Y be topologically complete metric spaces, let A ⊆ X be a non-σ-lower porous Suslin set and let B ⊆ Y be a non-σ-porous Suslin set. Then the product A × B is non-σ-lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non-σ-lower porous sets in topologically complete metric spaces.