# A characterization of the product of the rational numbers and complete Erd\H{o}s space

@article{HernandezGutierrez2021ACO, title={A characterization of the product of the rational numbers and complete Erd\H\{o\}s space}, author={Rodrigo Hern'andez-Guti'errez and A. Zaragoza}, journal={arXiv: General Topology}, year={2021} }

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… Expand

#### References

SHOWING 1-10 OF 21 REFERENCES

Erdos Space and Homeomorphism Groups of Manifolds

- Mathematics
- 2010

Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M. Consider the topological group \mathcal{H}(M,D) which… Expand

Characterizing Complete Erdős Space

- Mathematics
- Canadian Journal of Mathematics
- 2009

Abstract The space now known as complete Erdős space ${{\mathfrak{E}}_{\text{c}}}$ was introduced by Paul Erdős in 1940 as the closed subspace of the Hilbert space ${{\ell }^{2}}$ consisting of all… Expand

Symmetric products of Erdős space and complete Erdős space

- Mathematics
- 2020

Abstract It is shown that the symmetric products of complete Erdős space and Erdős space are homeomorphic to complete Erdős space and Erdős space, respectively. We will also give some properties of… Expand

The Infinite Dimensional Topology Of Function Spaces

- Computer Science
- 2016

The the infinite dimensional topology of function spaces is universally compatible with any devices to read, and an online access to it is set as public so you can download it instantly. Expand

Characterizing stable complete Erdős space

- Mathematics
- 2011

We focus on the space Ecω, the countable infinite power of complete Erdős space Ec. Both spaces are universal spaces for the class of almost zerodimensional spaces. We prove that Ecω has the property… Expand

On homogeneous totally disconnected 1-dimensional spaces

- 2007

The Cantor set and the set of irrational numbers are examples of 0dimensional, totally disconnected, homogeneous spaces which admit elegant characterizations and which play a crucial role in analysis… Expand

Complete Erdős space is unstable

- Mathematics
- Mathematical Proceedings of the Cambridge Philosophical Society
- 2004

It is proved that the countably infinite power of complete Erdős space $\Ec$ is not homeomorphic to $\Ec$. The method by which this result is obtained consists of showing that $\Ec$ does not contain… Expand

Steprāns, Complete Erdős space is unstable

- Math. Proc. Cambridge Philos. Soc
- 2004

The Infinite-Dimensional Topology of Function Spaces

- Mathematics
- 2001

Introduction. Chapter 1. Basic topology. Chapter 2. Basic combinatorial topology. Chapter 3. Basic dimension theory. Chapter 4. Basic ANR theory. Chapter 5. Basic infinite-dimensional topology.… Expand