A perfectly normal, locally compact, noncollectionwise normal space from ♢*

Daniels, Peg; Gruenhage, Gary

doi:10.1090/S0002-9939-1985-0796458-0

A perfectly normal, locally compact, noncollectionwise normal space from $\diamondsuit ^ \ast$
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by Peg Daniels and Gary Gruenhage

Proc. Amer. Math. Soc. 95 (1985), 115-118

DOI: https://doi.org/10.1090/S0002-9939-1985-0796458-0

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Abstract:

A perfectly normal, locally compact, collectionwise-${T_2}$, noncollectionwise normal space is constructed using ${\diamondsuit ^*}$, a combinatorial axiom which holds in Gödel’s constructible universe $L$. The construction answers questions of ${\text {F}}$. Tall and S. Watson.

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A note in general topology: if

then any normal space of character

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