1. Products of non-$\sigma $-lower porous sets
- Creator:
- Rmoutil, Martin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- topologically complete metric space, abstract porosity, $\sigma $-porous set, $\sigma $-lower porous set, and Cartesian product
- Language:
- English
- Description:
- In the present article we provide an example of two closed non-$\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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public