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On the non-productivity of normality in Moore spaces

Author(s): H. Cook; G. M. Reed
Journal: Proc. Amer. Math. Soc. 127 (1999), 875-880.
MSC (1991): Primary 54E30, 54D15, 54A35; Secondary 54B10, 54A10
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Abstract: Under Martin's Axiom and the denial of the Continuum Hypothesis, the authors give examples of normal Moore spaces whose squares are not normal.

References:

[AP1976]
K. Alster and T. C. Przymusi\'{n}ski, Normality and Martin's Axiom, Fund. Math. 91 (1976), 124-130. MR 54:3652

[C1968]
H. Cook, Cartesian products and continuous semi-metrics, Proc. of the Arizona State University Top. Conf. (1968), 58-63.

[C1976]
-, Cartesian products and continuous semi-metrics, II, preprint, 1976.

[CF1968]
H. Cook and B. Fitzpatrick, Inverse limits of perfectly normal Moore spaces, Proc. Amer. Math. Soc. 19 (1968), 189-192. MR 36:3306

[DS1979]
K. J. Devlin and S. Shelah, A note on the normal Moore space conjecture, Canad. J. Math. 31, 241-251. MR 81d:54022

[FT1966]
B. Fitzpatrick and D. R. Traylor, Two theorems on metrizability of Moore spaces, Pac. J. Math. 19 (1966), 259-264. MR 34:3535

[Fl1974]
W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298. MR 50:14682

[Fl1982]
-, Normal non-metrizable Moore space from continuum hypothesis or nonexistence of inner models with measurable cardinals, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), 1371-1372. MR 84f:54040

[Jo1937]
F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937), 671-677.

[K1948]
M. Katetov, Complete normality of Cartesian products, Fund. Math. 35 (1948), 271-274. MR 10:315h

[K1986]
K. Kunen, On ordinal-metric intersection topologies, Topology Appl. 22 (1986), 315-319. MR 87i:54046

[M1962]
R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ. 13, 1932 (revised edition, 1962). MR 27:709

[P1977]
T. C. Przymusi\'{n}ski, Normality and separability of Moore spaces, Set-Theoretic Topology, Acad. Press (NY, 1977), 325-337. MR 56:6617

[R1974a]
G. M. Reed, On chain conditions in Moore spaces, Gen. Top. and Appl. 4 (1974), 255-267. MR 49:9815

[R1974b]
-, On continuous images of Moore spaces, Canad. J. Math. 26 (1974), 1475-1479. MR 53:1530

[R1975]
-, On the productivity of normality in Moore spaces, Studies in Topology, Acad. Press (NY, 1975), 479-484. MR 53:1531

[R1986]
-, The intersection topology w.r.t. the real line and the countable ordinals, Trans. Amer. Math. Soc. 297 (1986), 509-520. MR 87m:54003

[R1990]
-, Set-theoretic problems in Moore spaces, Open Problems in Topology, North Holland (Amsterdam, 1990), 163-181.

[R$\infty$]
-, $Q$-sets, stationary sets in $\omega _1$, and normal Moore spaces, to appear.

[RZ1976]
G. M. Reed and P. L. Zenor, Metrization of Moore spaces and generalized manifolds, Fund. Math. 91 (1976), 213-220. MR 54:13868

[T1969]
F. D. Tall, Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Ph.D. thesis, University of Wisconsin, 1969; Dissert. Math. 148, 1-53. MR 56:13156

[T1984]
-, Normality versus collectionwise normality, Handbook of Set-Theoretic Topology (North Holland, 1984), 685-732. MR 86m:54022

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Additional Information:

H. Cook
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77004

G. M. Reed
Affiliation: St Edmund Hall, Oxford OX1 4AR, England
Email: mike.reed@comlab.ox.ac.uk

DOI: 10.1090/S0002-9939-99-04051-4
PII: S 0002-9939(99)04051-4
Keywords: Moore spaces, normality, products, Martin's Axiom, intersection topology.
Received by editor(s): March 6, 1991
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1999, American Mathematical Society

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