Reflection and Weakly Collectionwise Hausdorff Spaces

Tim LaBerge; Avner Landver

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Reflection and Weakly Collectionwise Hausdorff Spaces

Tim LaBerge·Avner Landver

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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 omega_2, first countable aleph_1-collectionwise Hausdorff spaces are weakly aleph_2-collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming E^omega_theta, a certain theta-family of integer valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to omega_2, these families do not exist.

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BibTeX RIS

Tim LaBerge, Avner Landver. 1992-10-21. Reflection and Weakly Collectionwise Hausdorff Spaces. https://arxiv.org/abs/math/9210203

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