Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A small Dowker space in ZFC

Author: Zoltan T. Balogh
Journal: Proc. Amer. Math. Soc. 124 (1996), 2555-2560
MSC (1991): Primary 54D15, 54D20
MathSciNet review: 1353374
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [B] Z. Balogh, There is a Q-set space in ZFC, Proc. Amer. Math. Soc. 113 (1991), 557-561. MR 91m:54046
  • [Be] M. Bell, On the combinatorial principle P(c), Fund. Math. 114 (1981), 137-145. MR 83e:03077
  • [C] P. deCaux, A collectionwise normal, weakly $\theta $-refinable Dowker space, Topology Proc. 1 (1976), 66-77. MR 56:6629
  • [D] C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), 219-224. MR 13:264c
  • [F] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294-298. MR 50:14682
  • [G] C. Good, Large cardinals and small Dowker spaces, Proc. Amer. Math. Soc. (to appear)
  • [JKR] I. Juhasz, K. Kunen, M. E. Rudin, Two more hereditarily separable non-Lindelof spaces, Canad. J. Math. 28 (1976), 998-1005. MR 55:1270
  • [K] K. Kunen, Set theory, North-Holland, 1980. MR 82f:03001
  • [KV] K. Kunen and J. E. Vaughan (eds.), Handbook of set-theoretic topology, North-Holland, 1984. MR 85k:54001
  • [R1] M. E. Rudin, Countable paracompactness and Souslin's problem, Canad. J. Math. 7 (1955), 543-547. MR 17:391e
  • [R2] M. E. Rudin, A normal space $X$ for which $X \times I$ is not normal, Fund. Math. 73 (1971), 179-186. MR 45:2660
  • [R3] M. E. Rudin, Two problems of Dowker, Proc. Amer. Math. Soc. 91 (1984), 155-158. MR 85i:54022b
  • [R4] M. E. Rudin, Dowker spaces, in Handbook of set-theoretic topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, 1984, pp. 761--781. MR 86c:54018
  • [R5] M. E. Rudin, A normal screenable nonparacompact space, Topology Appl. 15 (1983), 313-322. MR 84d:54042
  • [R6] M. E. Rudin, Some conjectures, in Open Problems in Topology (J. van Mill and G. M. Reed, eds.) North-Holland, 1990, pp. 183--193. MR 92e:54001
  • [S] S. Shelah, A consistent counterexample in the theory of collectionwise Hausdorff spaces, Israel J. Mathematics 65 (1989), 219-224. MR 90e:54087
  • [W1] S. Watson, A construction of a Dowker space, Proc. Amer. Math. Soc. 109 (1990), 835-841. MR 91b:54045
  • [W2] S. Watson, Problems I wish I could solve, in Open Problems in Topology (J. van Mill and G. M. Reed, eds.) North-Holland, 1990, pp. 37--76. MR 92e:54001
  • [We] W. Weiss, Small Dowker spaces, Pacific J. Math. 94 (1981), 485-492. MR 83d:54036

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54D15, 54D20

Retrieve articles in all journals with MSC (1991): 54D15, 54D20

Additional Information

Zoltan T. Balogh
Affiliation: Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056

Keywords: Small Dowker space, hereditarily normal, elementary submodel
Received by editor(s): March 23, 1994
Additional Notes: Research supported by NSF Grant DMS - 9108476.
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society