On the infinite powers of large zero-dimensional metrizable spaces
Andrea Medini

TL;DR
This paper proves that large powers of certain zero-dimensional metrizable spaces are strongly homogeneous, answering a question by Terada and improving previous results, with additional insights into partitioning such spaces into clopen sets.
Contribution
It demonstrates strong homogeneity of infinite powers of non-separable zero-dimensional metrizable spaces and advances understanding of their partition properties.
Findings
$X^$ is strongly homogeneous for non-separable zero-dimensional metrizable spaces.
Every non-compact weight-homogeneous metrizable space with a clopen c-base can be partitioned into c many clopen sets.
Improves previous results by van Engelen and partially answers Terada's question.
Abstract
We show that is strongly homogeneous whenever is a non-separable zero-dimensional metrizable space and 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 -base consisting of clopen sets can be partitioned into many clopen sets, where is the weight of . This improves a result of van Engelen.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Fixed Point Theorems Analysis · Advanced Banach Space Theory
