On the infinite powers of large zero-dimensional metrizable spaces

Abstract

We show that $X^{\hat{I}}»$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\hat{I}»$ is an infinite cardinal. This partially answers a question of Terada, and improves a previous result of the author. Along the way, we show that every non-compact weight-homogeneous metrizable space with a $\ddot{I}€$-base consisting of clopen sets can be partitioned into $\hat{I}º$ many clopen sets, where $\hat{I}º$ is the weight of $X$. This improves a result of van Engelen.

6 pages