有理数与完备Erdors空间乘积的一个刻划
A characterization of the product of the rational numbers and complete Erdős space
摘要：
Erdom s空间$\mathfrak{E}$和完备Erdom s空间$\mathfrak{E}_c$已经被证明具有拓扑特征。本文给出了拓扑空间$\mathbb{Q}\times\mathfrak{E}_c$的一个拓扑刻画，其中$\mathbb{Q}$是有理数空间.作为推论，我们证明了有限集$\mathcal{F}(\mathfrak{E}_c)$的Vietoris超空间同胚于$\mathbb{Q}\times\mathfrak{E}_c$ .我们还刻画了$\mathbb{Q}\times\mathfrak{E}_c$的因子。一个有趣的悬而未决的问题是，$σ{\mathfrak{E}_c}^ω$（$σ$ -$\mathfrak{E}_c$的可数个拷贝的产物）是否同胚于$\mathbb{Q}\times\mathfrak{E}_c$。
英文摘要：
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 $σ{\mathfrak{E}_c}^ω$, the $σ$-product of countably many copies of $\mathfrak{E}_c$, is homeomorphic to $\mathbb{Q}\times\mathfrak{E}_c$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
