Products of non-$\sigma$-lower porous sets

Rmoutil, Martin. "Products of non-$\sigma $-lower porous sets." Czechoslovak Mathematical Journal 63.1 (2013): 205-217. <http://eudml.org/doc/252491>.

@article{Rmoutil2013,
abstract = {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.},
author = {Rmoutil, Martin},
journal = {Czechoslovak Mathematical Journal},
keywords = {topologically complete metric space; abstract porosity; $\sigma $-porous set; $\sigma $-lower porous set; Cartesian product; lower porosity; -lower porosity},
language = {eng},
number = {1},
pages = {205-217},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Products of non-$\sigma $-lower porous sets},
url = {http://eudml.org/doc/252491},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Rmoutil, Martin
TI - Products of non-$\sigma $-lower porous sets
JO - Czechoslovak Mathematical Journal
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 1
SP - 205
EP - 217
AB - In the present article we provide an example of two closed non-$\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.
LA - eng
KW - topologically complete metric space; abstract porosity; $\sigma $-porous set; $\sigma $-lower porous set; Cartesian product; lower porosity; -lower porosity
UR - http://eudml.org/doc/252491
ER -