Sh:1025

• Juhász, I., & Shelah, S. (2015). Strong colorings yield \kappa-bounded spaces with discretely untouchable points. Proc. Amer. Math. Soc., 143(5), 2241–2247. arXiv: 1307.1989 DOI: 10.1090/S0002-9939-2014-12394-X MR: 3314130
• 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. Szentmiklóssy 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.
• published version (7p)

@article{Sh:1025,
 author = {Juh{\'a}sz, Istv{\'a}n and Shelah, Saharon},
 title = {{Strong colorings yield $\kappa$-bounded spaces with discretely untouchable points}},
 journal = {Proc. Amer. Math. Soc.},
 fjournal = {Proceedings of the American Mathematical Society},
 volume = {143},
 number = {5},
 year = {2015},
 pages = {2241--2247},
 issn = {0002-9939},
 mrnumber = {3314130},
 mrclass = {54A25 (03E05 54D30)},
 doi = {10.1090/S0002-9939-2014-12394-X},
 note = {\href{https://arxiv.org/abs/1307.1989}{arXiv: 1307.1989}},
 arxiv_number = {1307.1989}
}