Symmetric products of Erdős space and complete Erdős space

完备 Erdős 空间的 σ-积

The $σ$-product of complete Erdős space

本文证明完备 Erdős 空间的 σ-积与有理数积同胚，解决了 Hernández-Gutiérrez 和 Zaragoza 提出的问题。

A characterization of the product of the rational numbers and complete Erdős space

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 $σ{\mathfrak{E}_c…