On the non-productivity of normality in Moore spaces
HTML articles powered by AMS MathViewer
- by H. Cook and G. M. Reed PDF
- Proc. Amer. Math. Soc. 127 (1999), 875-880 Request permission
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
- K. Alster and T. Przymusiński, Normality and Martin’s axiom, Fund. Math. 91 (1976), no. 2, 123–131. MR 415567, DOI 10.4064/fm-91-2-123-131
- H. Cook, Cartesian products and continuous semi-metrics, Proc. of the Arizona State University Top. Conf. (1968), 58–63.
- —, Cartesian products and continuous semi-metrics, II, preprint, 1976.
- Howard Cook and Ben Fitzpatrick Jr., Inverse limits of perfectly normal spaces, Proc. Amer. Math. Soc. 19 (1968), 189–192. MR 220240, DOI 10.1090/S0002-9939-1968-0220240-6
- Keith J. Devlin and Saharon Shelah, A note on the normal Moore space conjecture, Canadian J. Math. 31 (1979), no. 2, 241–251. MR 528801, DOI 10.4153/CJM-1979-025-8
- Ben Fitzpatrick Jr. and D. R. Traylor, Two theorems on metrizability of Moore spaces, Pacific J. Math. 19 (1966), 259–264. MR 203686, DOI 10.2140/pjm.1966.19.259
- William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4
- 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
- F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937), 671–677.
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- Kenneth Kunen, On ordinal-metric intersection topologies, Topology Appl. 22 (1986), no. 3, 315–319. MR 842665, DOI 10.1016/0166-8641(86)90030-1
- R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
- Teodor C. Przymusiński, Normality and separability of Moore spaces, Set-theoretic topology (Papers, Inst. Medicine and Math., Ohio Univ., Athens, Ohio, 1975–1976) Academic Press, New York, 1977, pp. 325–337. MR 0448310
- G. M. Reed, On chain conditions in Moore spaces, General Topology and Appl. 4 (1974), 255–267. MR 345076, DOI 10.1016/0016-660X(74)90025-7
- G. M. Reed, On continuous images of Moore spaces, Canadian J. Math. 26 (1974), 1475–1479. MR 397672, DOI 10.4153/CJM-1974-142-3
- G. M. Reed, On the productivity of normality in Moore spaces, Studies in topology (Proc. Conf., Univ. North Carolina, Charlotte, N.C., 1974; dedicated to Math. Sect. Polish Acad. Sci.), Academic Press, New York, 1975, pp. 479–484. MR 0397673
- G. M. Reed, The intersection topology w.r.t. the real line and the countable ordinals, Trans. Amer. Math. Soc. 297 (1986), no. 2, 509–520. MR 854081, DOI 10.1090/S0002-9947-1986-0854081-9
- —, Set-theoretic problems in Moore spaces, Open Problems in Topology, North Holland (Amsterdam, 1990), 163–181.
- —, $Q$-sets, stationary sets in $\omega _1$, and normal Moore spaces, to appear.
- G. M. Reed and P. L. Zenor, Metrization of Moore spaces and generalized manifolds, Fund. Math. 91 (1976), no. 3, 203–210. MR 425918, DOI 10.4064/fm-91-3-203-210
- F. D. Tall, Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Dissertationes Math. (Rozprawy Mat.) 148 (1977), 53. MR 454913
- Franklin D. Tall, Normality versus collectionwise normality, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 685–732. MR 776634
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
- Received by editor(s): March 6, 1991
- Communicated by: Franklin D. Tall
- © Copyright 1999 American Mathematical Society
- 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