# 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.
• 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)
Bib entry
@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}
}