Products and h-homogeneity

2009/11/05 by Medini, Andrea
#54B10 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.0911.1023

Abstract

Building on work of Terada, we prove that h-homogeneity is productive in the class of zero-dimensional spaces. Then, by generalizing a result of Motorov, we show that for every non-empty zero-dimensional space X there exists a non-empty zero-dimensional space Y such that X× Y is h-homogeneous. Also, we simultaneously generalize results of Motorov and Terada by showing that if X is a space such that the isolated points are dense then X^κ is h-homogeneous for every infinite cardinal κ. Finally, we show that a question of Terada (whether X^ω is h-homogeneous for every zero-dimensional first-countable X) is equivalent to a question of Motorov (whether such an infinite power is always divisible by 2) and give some partial answers.

Related

• Products and countable dense homogeneity
• Countable dense homogeneity in powers of zero-dimensional definable\n spaces
• Countable dense homogeneity in large products of Polish spaces
• Zero-dimensional σ-homogeneous spaces
• Every zero-dimensional homogeneous space is strongly homogeneous under determinacy