A small Dowker space in ZFC

Balogh, Zoltan

doi:10.1090/S0002-9939-96-03610-6

A small Dowker space in ZFC
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by Zoltan T. Balogh PDF

Proc. Amer. Math. Soc. 124 (1996), 2555-2560 Request permission

Abstract:

We construct a hereditarily normal topological space whose product with the unit interval is not normal. The space is $\sigma$-relatively discrete and has cardinality of the continuum $\mathfrak {c}$.

References

Zoltán T. Balogh, There is a $Q$-set space in ZFC, Proc. Amer. Math. Soc. 113 (1991), no. 2, 557–561. MR 1077786, DOI 10.1090/S0002-9939-1991-1077786-3
Murray G. Bell, On the combinatorial principle $P({\mathfrak {c}})$, Fund. Math. 114 (1981), no. 2, 149–157. MR 643555, DOI 10.4064/fm-114-2-149-157
Peter de Caux, A collectionwise normal weakly $\theta$-refinable Dowker space which is neither irreducible nor realcompact, Topology Proceedings, Vol. I (Conf., Auburn Univ., Auburn, Ala., 1976) Math. Dept., Auburn Univ., Auburn, Ala., 1977, pp. 67–77. MR 0448322
C. J. Everett Jr., Annihilator ideals and representation iteration for abstract rings, Duke Math. J. 5 (1939), 623–627. MR 13
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
C. Good, Large cardinals and small Dowker spaces, Proc. Amer. Math. Soc. (to appear)
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
Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam-New York, 1980. An introduction to independence proofs. MR 597342
Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland Publishing Co., Amsterdam, 1984. MR 776619
Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
Mary Ellen Rudin, A normal space $X$ for which $X\times I$ is not normal, Fund. Math. 73 (1971/72), no. 2, 179–186. MR 293583, DOI 10.4064/fm-73-2-179-186
Mary Ellen Rudin, Dowker’s set theory question, Questions Answers Gen. Topology 1 (1983), no. 2, 75–76. MR 722085
Mary Ellen Rudin, Dowker spaces, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 761–780. MR 776636
Mary Ellen Rudin, A normal screenable nonparacompact space, Topology Appl. 15 (1983), no. 3, 313–322. MR 694550, DOI 10.1016/0166-8641(83)90061-5
E. M. Vechtomov, Questions on the determination of topological spaces by algebraic systems of continuous functions, Algebra. Topology. Geometry, Vol. 28 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990, pp. 3–46 (Russian). Translated in J. Soviet Math. 53 (1991), no. 2, 123–147. MR 1059476
S. Shelah, A consistent counterexample in the theory of collectionwise Hausdorff spaces, Israel J. Math. 65 (1989), no. 2, 219–224. MR 998672, DOI 10.1007/BF02764862
Stephen Watson, A construction of a Dowker space, Proc. Amer. Math. Soc. 109 (1990), no. 3, 835–841. MR 1019285, DOI 10.1090/S0002-9939-1990-1019285-X
E. M. Vechtomov, Questions on the determination of topological spaces by algebraic systems of continuous functions, Algebra. Topology. Geometry, Vol. 28 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1990, pp. 3–46 (Russian). Translated in J. Soviet Math. 53 (1991), no. 2, 123–147. MR 1059476
W. Weiss, Small Dowker spaces, Pacific J. Math. 94 (1981), no. 2, 485–492. MR 628595, DOI 10.2140/pjm.1981.94.485