Strong colorings yield kappa-bounded spaces with discretely untouchable\n points

2013/07/08 by István Juhász, Saharon Shelah, Juhasz, Istvan +1
Mathematics · #03E35 #54A25 #54A35 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1307.1989

openalex publication_date 2013/07/08 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

It is well-known that every non-isolated point in a compact Hausdorff space\nis the accumulation point of a discrete subset. Answering a question raised by\nZ. Szentmiklossy and the first author, we show that this statement fails for\ncountably compact regular spaces, and even for omega-bounded regular spaces. In\nfact, there are kappa-bounded counterexamples for every infinite cardinal\nkappa. The proof makes essential use of the so-called 'strong colorings' that\nwere invented by the second author.\n

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