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Paranormal spaces under $\diamondsuit ^{*}$


Authors: Kerry D. Smith and Paul J. Szeptycki
Journal: Proc. Amer. Math. Soc. 128 (2000), 903-908
MSC (1991): Primary 54B10, 54D15, 54D20, 03E35, 03E45
DOI: https://doi.org/10.1090/S0002-9939-99-05032-7
Published electronically: May 6, 1999
MathSciNet review: 1622981
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Abstract | References | Similar Articles | Additional Information

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).


References [Enhancements On Off] (What's this?)

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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: https://doi.org/10.1090/S0002-9939-99-05032-7
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
Published electronically: May 6, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society

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