A characterization of the product of the rational numbers and complete Erdős space
Abstract
Erdős space $\mathfrak{E}$ and complete Erdős space $\mathfrak{E}_c$ have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space $\mathbb{Q}\times\mathfrak{E}_c$, where $\mathbb{Q}$ is the space of rational numbers. As a corollary, we show that the Vietoris hyperspace of finite sets $\mathcal{F}(\mathfrak{E}_c)$ is homeomorphic to $\mathbb{Q}\times\mathfrak{E}_c$. We also characterize the factors of $\mathbb{Q}\times\mathfrak{E}_c$. An interesting open question that is left open is whether $\sigma{\mathfrak{E}_c}^\omega$, the $\sigma$product of countably many copies of $\mathfrak{E}_c$, is homeomorphic to $\mathbb{Q}\times\mathfrak{E}_c$.
 Publication:

arXiv eprints
 Pub Date:
 February 2021
 arXiv:
 arXiv:2103.00102
 Bibcode:
 2021arXiv210300102H
 Keywords:

 Mathematics  General Topology;
 54F65;
 54F50;
 54A10;
 54B20;
 54H05