Paranormal spaces under ♢*
Kerry D. Smith, Paul J. Szeptycki · Proceedings of the American Mathematical Society · 1999
We prove that paranormal spaces of character ≤ ω 1 \leq \omega _{1} are ω 1 \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).