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On cohesive almost zero-dimensional spaces
Published online by Cambridge University Press: 15 July 2020
Abstract
We investigate C-sets in almost zero-dimensional spaces, showing that closed
$\sigma $
C-sets are C-sets. As corollaries, we prove that every rim-
$\sigma $
-compact almost zero-dimensional space is zero-dimensional and that each cohesive almost zero-dimensional space is nowhere rational. To show that these results are sharp, we construct a rim-discrete connected set with an explosion point. We also show that every cohesive almost zero-dimensional subspace of
$($
Cantor set
$)\!\times \mathbb R$
is nowhere dense.
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- © Canadian Mathematical Society 2020
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