Juhász, István and Shelah, S. (2015) STRONG COLORINGS YIELD kappa-BOUNDED SPACES WITH DISCRETELY UNTOUCHABLE POINTS. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 143 (5). pp. 2241-2247. ISSN 0002-9939
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Official URL: http://dx.doi.org/10.1090/S0002-9939-2014-12394-X
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.
| Item Type: | Article |
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| Uncontrolled Keywords: | Resolvability; kappa-bounded spaces; discretely untouchable points; Strong colorings; κ-bounded spaces |
| Subjects: | Q Science / természettudomány > QA Mathematics / matematika |
| SWORD Depositor: | MTMT SWORD |
| Depositing User: | MTMT SWORD |
| Date Deposited: | 17 Feb 2016 11:08 |
| Last Modified: | 17 Feb 2016 11:08 |
| URI: | http://real.mtak.hu/id/eprint/33644 |
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