Geodesic
Products of non-$\sigma $-lower porous sets
Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 205-217
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In the present article we provide an example of two closed non-$\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 $-lower porous sets in topologically complete metric spaces.
In the present article we provide an example of two closed non-$\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.
DOI : 10.1007/s10587-013-0014-4
Classification : 28A05, 54B10, 54E35, 54G20
Keywords: topologically complete metric space; abstract porosity; $\sigma $-porous set; $\sigma $-lower porous set; Cartesian product 
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Rmoutil, Martin. Products of non-$\sigma $-lower porous sets. Czechoslovak Mathematical Journal, Tome 63 (2013) no. 1, pp. 205-217. doi: 10.1007/s10587-013-0014-4

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