Reflection and weakly collectionwise hausdorff spaces

Abstract

We show that (θ) implies that there is a first countable < θ- 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 collectionwise Hausdorff spaces are weakly collectionwise Hausdorff (weakly collectionwise Hausdorff). In the last section we show that assuming a certain θ-family of integer-valued functions exists and that in the model obtained by Levy collapsing a supercompact cardinal to ω these families do not exist. © 1994 American Mathematical Society.