On the infinite powers of large zero-dimensional metrizable spaces
Keywords:
zero-dimensional, metrizable, infinite power, strongly homogeneous, h-homogeneous, clopen set, partition, $\pi$-baseAbstract
We show that $X^\lambda$ is strongly homogeneous whenever $X$ is a non-separable zero-dimensional metrizable space and $\lambda$ 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 $\pi$-base consisting of clopen sets can be partitioned into $\kappa$ many clopen sets, where $\kappa$ is the weight of $X$. This improves a result of van Engelen.
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