Reflection and Weakly Collectionwise Hausdorff Spaces
Tim LaBerge, Avner Landver
Abstract
We show that square(theta) implies that there is a first countable <theta-collectionwise Hausdorff space that is not weakly theta-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact (supercompact) cardinal to omega2, first countable aleph1-collectionwise Hausdorff spaces are weakly aleph2-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming Eomegatheta, a certain theta-family of integer valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to omega2, these families do not exist.
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