A normal screenable

nonparacompact space in ZFC

Author:
Zoltan T. Balogh

Journal:
Proc. Amer. Math. Soc. **126** (1998), 1835-1844

MSC (1991):
Primary 54D15, 54D20; Secondary 54G20

DOI:
https://doi.org/10.1090/S0002-9939-98-04425-6

MathSciNet review:
1459105

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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a normal, screenable, nonparacompact space in ZFC. The existence of such a space is also known to imply that there is a normal, screenable space which is not collectionwise normal.

**[B]**R.H. Bing,*Metrization of Topological Spaces*, Canad. J. Math.**3**(1951), 175-186. MR**13:264f****[D]**C.H. Dowker,*On Countably Paracompact Spaces*, Canad. J. Math.**3**(1951), 219-224. MR**13:264c****[KV]**K. Kunen and J.E. Vaughan, eds.,*Handbook of Set-theoretic Topology*, North-Holland, 1984. MR**85k:54001****[N]**K. Nagami,*Paracompactness and strong screenability*, Nagoya Math. J.**8**(1955), 83-88. MR**16:1138d****[R1]**M.E. Rudin,*A Normal, Screenable, Non-paracompact Space*, Topology Appl.**15**(1983), 313-322. MR**84d:54042****[R2]**M.E. Rudin,*Collectionwise Normality in Screenable Spaces*, PAMS**87**(1983), 347-350. MR**84a:54038****[T1]**F.D. Tall,*Normality versus Collectionwise Normality*, Handbook of Set-theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, 1984, pp. 685-732. MR**86m:54022****[T2]**F.D. Tall,*Tall's Problems*, Open Problems in Topology (J. van Mill, G.M. Reed, eds.), North-Holland, 1990, pp. 21-35. MR**92c:54001****[TP]***Topology Proceedings*, vol. 1, 1976, pp. 363-364, Problem Section.**[W]**S. Watson,*Problems I wish I could solve*, Open Problems in Topology (J. van Mill and G.M. Reed, eds.), North-Holland, 1990, pp. 37-76. MR**92c:54001**

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Additional Information

**Zoltan T. Balogh**

Affiliation:
Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45058

Email:
ZTBalogh@miavx1.muohio.edu

DOI:
https://doi.org/10.1090/S0002-9939-98-04425-6

Keywords:
Normal,
screenable,
paracompact,
collectionwise normal

Received by editor(s):
March 5, 1996

Additional Notes:
The author’s research was partially supported by NSF Grant DMS-9623391

Communicated by:
Franklin D. Tall

Article copyright:
© Copyright 1998
American Mathematical Society