On the infinite powers of large zero-dimensional metrizable spaces

2025/01/13 by Andrea Medini, Medini, Andrea · 1 voice · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #Fixed Point Theorems Analysis #math.GN

paper · pdf · doi:10.48550/arxiv.2501.07253

arxiv published 2025/01/13 · arxiv updated 2025/08/16

Abstract

We show that X^λ is strongly homogeneous whenever X is a non-separable zero-dimensional metrizable space and λ 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 π-base consisting of clopen sets can be partitioned into κ many clopen sets, where κ is the weight of X. This improves a result of van Engelen.

Cited by

• The two-disjoint-copies property for compact spaces, homogeneity and connection with C_p-theory

Discussions

• Andrea Medini: On the infinite powers of large zero-dimensional metrizable spaces https://arxiv.org/abs/2501.07253 https://arxiv.org/pdf/2501.07253 https://arxiv.org/html/2501.07253 [bsky, 0 points, 1 comments]

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