Strong colorings yield $\kappa$-bounded spaces with discretely untouchable points
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- by István Juhász and Saharon Shelah PDF
- Proc. Amer. Math. Soc. 143 (2015), 2241-2247 Request permission
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.References
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Additional Information
- István Juhász
- Affiliation: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, 13-15 Reáltanoda u. 1053 Budapest, Hungary
- Email: juhasz@renyi.hu
- Saharon Shelah
- Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Har ha-Tsofim, Jerusalem, Israel
- MR Author ID: 160185
- ORCID: 0000-0003-0462-3152
- Email: shelah@math.huji.ac.il
- Received by editor(s): June 25, 2013
- Received by editor(s) in revised form: October 14, 2013
- Published electronically: December 22, 2014
- Additional Notes: The first author was partially supported by OTKA grant no. K 83726
- Communicated by: Mirna Džamonja
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 2241-2247
- MSC (2010): Primary 54A25, 03E05, 54D30
- DOI: https://doi.org/10.1090/S0002-9939-2014-12394-X
- MathSciNet review: 3314130