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On the non-productivity
of normality in Moore spaces


Authors: H. Cook and G. M. Reed
Journal: Proc. Amer. Math. Soc. 127 (1999), 875-880
MSC (1991): Primary 54E30, 54D15, 54A35; Secondary 54B10, 54A10
DOI: https://doi.org/10.1090/S0002-9939-99-04051-4
MathSciNet review: 1415580
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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.


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  • [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: https://doi.org/10.1090/S0002-9939-99-04051-4
Keywords: Moore spaces, normality, products, Martin's Axiom, intersection topology.
Received by editor(s): March 6, 1991
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1999 American Mathematical Society

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