Strong colorings yield kappa-bounded spaces with discretely untouchable points

Istvan Juhasz; Saharon Shelah

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arXiv · 1307.1989

Strong colorings yield kappa-bounded spaces with discretely untouchable points

Istvan Juhasz·Saharon Shelah

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Abstract

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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Istvan Juhasz, Saharon Shelah. 2013-07-08. Strong colorings yield kappa-bounded spaces with discretely untouchable points. https://arxiv.org/abs/1307.1989

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