### Strong colorings yield $\kappa$-bounded spaces with discretely untouchable points

by Juhasz and Shelah. [JuSh:1025]

Proc AMS, 2015

It is well-known that every non-isolated point in a
compact Hausdorff space is the accumulation point of a
discrete subset. Answering a question raised by
Z. Szentmiklossy and the first author. We show that
this statement fails for countably compact regular spaces,
and
even for omega-bounded regular spaces. In fact, there are
kappa-bounded
counterexamples for every
infinite cardinal kappa . The proof makes essential use
of the so-called strong colorings that were
invented by the second author.

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