Hereditarily strongly cwH and separation axioms
by
Peter Nyikos
University of South Carolina

Inspired by some powerful consistency results of the late Zoltan Balogh and the speaker, we ask whether it is consistent that every locally compact, hereditarily strongly collectionwise Hausdorff (cwH) space is (hereditarily) normal, and whether ``locally compact'' can be weakened to ``regular''. A modification of the neighborhoods of the origin in the Euclidean plane gives a nice example of a hereditarily strongly cwH space that is not regular. A consistent locally compact, non-normal example can be obtained by taking X ×\omega+1 where X is a hereditarily normal, locally compact Dowker space obtained by the speaker from \diamondsuit [Topology Proceedings 24 (1999) 261-276].

Date received: February 24, 2003