Paranormal spaces under ♢*

Smith, Kerry; Szeptycki, Paul

doi:10.1090/S0002-9939-99-05032-7

Paranormal spaces under $\diamondsuit ^{*}$
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by Kerry D. Smith and Paul J. Szeptycki PDF

Proc. Amer. Math. Soc. 128 (2000), 903-908 Request permission

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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