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Keywords:
topologically complete metric space; abstract porosity; $\sigma $-porous set; $\sigma $-lower porous set; Cartesian product
topologically complete metric space; abstract porosity; $\sigma $-porous set; $\sigma $-lower porous set; Cartesian product
Summary:
In the present article we provide an example of two closed non-$\sigma $-lower porous sets $A, B \subseteq \mathbb R $ such that the product $A\times B$ is lower porous. On the other hand, we prove the following: Let $X$ and $Y$ be topologically complete metric spaces, let $A\subseteq X$ be a non-$\sigma $-lower porous Suslin set and let $B\subseteq Y$ be a non-$\sigma $-porous Suslin set. Then the product $A\times B$ is non-$\sigma $-lower porous. We also provide a brief summary of some basic properties of lower porosity, including a simple characterization of Suslin non-$\sigma $-lower porous sets in topologically complete metric spaces.
References:
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