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

Abstract

Erdős space E and complete Erdős space Ec have been previously shown to have topological characterizations. In this paper, we provide a topological characterization of the topological space Q × Ec, where Q is the space of rational numbers. As a corollary, we show that the Vietoris hyperspace of finite sets F (Ec) is homeomorphic to Q × Ec. We also characterize the factors of Q × Ec. An interesting open question that is left open is whether σE ω c , the σ-product of countably many copies of Ec, is homeomorphic to Q × Ec.