The $\sigma$-product of complete Erd\H{o}s space

TL;DR

This paper proves that the $\sigma$-product of complete Erdős space is homeomorphic to the product of the rationals and Erdős space, resolving a previously posed question in topology.

Contribution

It establishes a homeomorphism between the $\sigma$-product of complete Erdős space and the rational product, providing a new understanding of their topological relationship.

Findings

The $\sigma$-product of complete Erdős space is homeomorphic to $Q imes ext{Erdős space}.

Answers a question by Hernádez-Gutiérrez and Zaragoza about the structure of this $\sigma$-product.

Enhances understanding of the topological properties of Erdős space and its products.

Abstract

We show that the $\sigma$-product of complete Erd\H{o}s space $\mathfrak E_{\mathrm{c}}$ is homeomorphic to the rational product $\mathbb Q\times \mathfrak E_{\mathrm{c}}$, answering a question by Rodrigo Hern\'{a}ndez-Guti\'{e}rrez and Alfredo Zaragoza.