Symmetric products of Erd\H{o}s space and complete Erd\H{o}s space

TL;DR

This paper proves that symmetric products of Erdős space and complete Erdős space are homeomorphic to the original spaces, and explores properties of their hyperspaces of compact subsets with the Vietoris topology.

Contribution

It establishes the homeomorphism of symmetric products of Erdős spaces with the original spaces and investigates their hyperspace properties.

Findings

Symmetric products of Erdős space are homeomorphic to Erdős space.

Symmetric products of complete Erdős space are homeomorphic to complete Erdős space.

Properties of hyperspaces of compact subsets with Vietoris topology are analyzed.

Abstract

It is shown that the symmetric products of complete Erd\H{o}s space and Erd\H{o}s space are homeomorphic to complete Erd\H{o}s space and Erd\H{o}s space, respectively. We will also give some properties of their hyperspace of compact subsets with the Vietoris topology.