Abstract
It is shown to be consistent that there is a normal first countable locally countable space which is not collectionwise Hausdorff and in which there is a closed discrete non-G δ set which provides the counterexample to collectionwise Hausdorffness. This answers a question of P. Nyikos.
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References
P. Nyikos, inHandbook of Set Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 633–684.
S. Shelah,Whitehead groups may not be free, even assuming CH, I, Isr. J. Math.28 (1977), 193–204.
S. Shelah,Whitehead groups may or may not be free, even assuming CH, II, Isr. J. Math.35 (1980), 257–285.
S. Shelah,Proper Forcing, Lecture Notes in Math.940, Springer-Verlag, Berlin, 1982.
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Publication 349, partially supported by the BSF.
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Shelah, S. A consistent counterexample in the theory of collectionwise Hausdorff spaces. Israel J. Math. 65, 219–224 (1989). https://doi.org/10.1007/BF02764862
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DOI: https://doi.org/10.1007/BF02764862