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On some problems in general topology. (English) Zbl 0847.54004
Bartoszyński, Tomek (ed.) et al., Set theory. Annual Boise extravaganza in set theory (BEST) conference, 1992/1994, Boise State University, Boise, ID, USA. Providence, RI: American Mathematical Society. Contemp. Math. 192, 91-101 (1996).
This paper (finally) publishes, for the first time, the author’s proof of three results from 1977 which are by now so well-known (the results, not the proofs) that it is very surprising to learn that they were not published before. The first is that there is, in ZFC, a discrete subset of \( \beta \mathbb{N}\) with cardinality \(\aleph_1\) which is not \(C^*\)-embedded. The second result is that it is consistent with Martin’s Axiom that any discrete subset of \(\beta \mathbb{N}\) of size \(\aleph_1\) is \(C^*\)-embedded if it can simply be separated by disjoint open sets. The third result is the consistency of there being a Lindelöf space with points \(G_\delta\) which has cardinality greater than the continuum.
For the entire collection see [Zbl 0832.00031].
Reviewer: A.Dow (North York)

MSC:
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
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