  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.
