Strong colorings yield kappa-bounded spaces with discretely untouchable points
General Topology
2013-07-09 v1
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.
Keywords
Cite
@article{arxiv.1307.1989,
title = {Strong colorings yield kappa-bounded spaces with discretely untouchable points},
author = {Istvan Juhasz and Saharon Shelah},
journal= {arXiv preprint arXiv:1307.1989},
year = {2013}
}