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# Reflection and Weakly Collectionwise Hausdorff Spaces

Tim Laberge and Avner Landver
Proceedings of the American Mathematical Society
Vol. 122, No. 1 (Sep., 1994), pp. 291-302
DOI: 10.2307/2160874
Stable URL: http://www.jstor.org/stable/2160874
Page Count: 12
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## Abstract

We show that □(θ) implies that there is a first countable $< \theta$-collectionwise Hausdorff space that is not weakly θ-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to ω2, first countable ℵ1-collectionwise Hausdorff spaces are weakly ℵ2-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming Eω θ, a certain θ-family of integer-valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to ω2, these families do not exist.

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