# 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)

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}, doi = {10.1090/S0002-9939-2014-12394-X}, mrclass = {54A25 (03E05 54D30)}, mrnumber = {3314130}, mrreviewer = {Wanjun Hu}, doi = {10.1090/S0002-9939-2014-12394-X}, note = {\href{https://arxiv.org/abs/1307.1989}{arXiv: 1307.1989}}, arxiv_number = {1307.1989} }