A solution of a problem about Erdös Space

Abstract

For Erdős space, $\mathfrak{E}$, let us define a topology, ${\tau }_{clopen}$, which is generated by clopen subsets of $\mathfrak{E}$. A. V. Arhangel'skii and J. Van Mill asked whether the topology ${\tau }_{clopen}$ is compatible with the group structure on $\mathfrak{E}$. In this paper, we give a negative answer for this question.

6 pages