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Products and h-homogeneity
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 there exists a
non-empty zero-dimensional space such that is h-homogeneous.
Also, we simultaneously generalize results of Motorov and Terada by showing
that if is a space such that the isolated points are dense then
is h-homogeneous for every infinite cardinal . Finally, we show that a
question of Terada (whether is h-homogeneous for every
zero-dimensional first-countable ) is equivalent to a question of Motorov
(whether such an infinite power is always divisible by 2) and give some partial
answers.Comment: 10 page
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