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 $\diamondsuit ^ \ast$
HTML articles powered by AMS MathViewer

by Peg Daniels and Gary Gruenhage PDF

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

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.

References

William G. Fleissner, Normal nonmetrizable Moore space from continuum hypothesis or nonexistence of inner models with measurable cardinals, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 4, 1371–1372. MR 648069, DOI 10.1073/pnas.79.4.1371
I. Juhász, K. Kunen, and M. E. Rudin, Two more hereditarily separable non-Lindelöf spaces, Canadian J. Math. 28 (1976), no. 5, 998–1005. MR 428245, DOI 10.4153/CJM-1976-098-8
Peter J. Nyikos, A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1980), no. 3, 429–435. MR 553389, DOI 10.1090/S0002-9939-1980-0553389-4

A note in general topology: if

then any normal space of character

Franklin D. Tall, Collectionwise normality without large cardinals, Proc. Amer. Math. Soc. 85 (1982), no. 1, 100–102. MR 647907, DOI 10.1090/S0002-9939-1982-0647907-7
W. Stephen Watson, Locally compact normal spaces in the constructible universe, Canadian J. Math. 34 (1982), no. 5, 1091–1096. MR 675681, DOI 10.4153/CJM-1982-078-8