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Paranormal spaces under $\diamondsuit ^{*}$

Author(s): Kerry D. Smith; Paul J. Szeptycki
Journal: Proc. Amer. Math. Soc. 128 (2000), 903-908.
MSC (1991): Primary 54B10, 54D15, 54D20, 03E35, 03E45
Posted: May 6, 1999
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Abstract: We prove that paranormal spaces of character $\leq \omega _{1}$ are $\omega _{1}$-
collectionwise Hausdorff assuming the set-theoretic principle $\diamondsuit ^{*}$. This gives an affirmative answer to problem 197 in Problems I wish I could solve, by W. S. Watson (Open Problems in Topology (1990), 37-76).

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Additional Information:

Kerry D. Smith
Affiliation: Department of Mathematical Sciences, Franklin College, Franklin, Indiana 46131-2598
Email: smithk@franklincoll.edu

Paul J. Szeptycki
Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701-2979
Email: szeptyck@bing.math.ohiou.edu

DOI: 10.1090/S0002-9939-99-05032-7
PII: S 0002-9939(99)05032-7
Keywords: $\diamondsuit ^{*}$, paranormal, first countable, $\omega _{1}$-collectionwise Hausdorff
Received by editor(s): August 21, 1997
Received by editor(s) in revised form: April 20, 1998
Posted: May 6, 1999
Communicated by: Alan Dow
Copyright of article: Copyright 1999, American Mathematical Society

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