arXiv subjects

Alfredo Zaragoza

Publications and source records attributed to Alfredo Zaragoza.

4 recordsLinked to original sources

arXiv2022

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

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 $\mathbb{Q}\times\mathfrak{E}_c$.

math.GN↗

arXiv2022

Hyperspaces of dimension 1

In a previuos paper the author asked if there exists a one-dimensional space $X$ that is not almost zero-dimensional, such that the dimension of the hyperspace of compact subsets of $X$ is one-dimensional. In this short note we give examples of spaces $X$ that are not almost zero-dimensional such that $X$ is one-dimensional and their hyperspace of compacta of $X$ also is one-dimensional.

math.GN↗

arXiv2020

The Vietoris hyperspace of finite sets of Erdős space

Recently, David S. Lipham has shown that if $X$ is an Erdős space factor then the Vietoris hyperspace $\mathcal{F}(X)$ of finite subsets of $X$ is an Erdős space factor. In this short note we prove that if $\mathfrak{E}$ denotes Erdős space then $\mathcal{F}(\mathfrak{E})$ is in fact homeomorphic to $\mathfrak{E}$.

math.GN↗

arXiv2020

Symmetric products of Erdős space and complete Erdős space

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 their hyperspace of compact subsets with the Vietoris topology.

math.GN↗