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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