Metacompact subspaces of products of ordinals
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- by William G. Fleissner
- Proc. Amer. Math. Soc. 130 (2002), 293-301
- DOI: https://doi.org/10.1090/S0002-9939-01-06026-9
- Published electronically: May 25, 2001
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Abstract:
Let $X$ be a subspace of the product of finitely many ordinals. $X$ is countably metacompact, and $X$ is metacompact iff $X$ has no closed subset homeomorphic to a stationary subset of a regular uncountable cardinal. A theorem generalizing these two results is: $X$ is $\lambda$-metacompact iff $X$ has no closed subset homeomorphic to a $(\kappa _1, \ldots , \kappa _n)$-stationary set where $\kappa _1 < \lambda$.References
- Eric K. van Douwen and David J. Lutzer, A note on paracompactness in generalized ordered spaces, Proc. Amer. Math. Soc. 125 (1997), no. 4, 1237–1245. MR 1396999, DOI 10.1090/S0002-9939-97-03902-6
- Sergio Sispanov, Generalización del teorema de Laguerre, Bol. Mat. 12 (1939), 113–117 (Spanish). MR 3
- Fleissner, W. and Stanley, A. D-spaces, to appear, Topol. Appl.
- William G. Fleissner, If all normal Moore spaces are metrizable, then there is an inner model with a measurable cardinal, Trans. Amer. Math. Soc. 273 (1982), no. 1, 365–373. MR 664048, DOI 10.1090/S0002-9947-1982-0664048-8
- Fleissner, W. Normal Moore spaces, Set Theoretic Topology, ed by Kunen & Vaughan Elsevier, 1984 pp.423-501
- Nobuyuki Kemoto, Tsugunori Nogura, Kerry D. Smith, and Yukinobu Yajima, Normal subspaces in products of two ordinals, Fund. Math. 151 (1996), no. 3, 279–297. MR 1424577
- Nobuyuki Kemoto and Kerry D. Smith, The product of two ordinals is hereditarily countably metacompact, Proceedings of the International Conference on Set-theoretic Topology and its Applications (Matsuyama, 1994), 1996, pp. 91–96. MR 1425929, DOI 10.1016/S0166-8641(96)00047-8
- Nobuyuki Kemoto and Kerry D. Smith, Hereditary countable metacompactness in finite and infinite product spaces of ordinals, Topology Appl. 77 (1997), no. 1, 57–63. MR 1443428, DOI 10.1016/S0166-8641(96)00106-X
- Kemoto, N., Tamano, K., and Yajima, Y. Generalized paracompactness of subspaces in products of two ordinals, to appear, Topol. Appl. 104(2000)155–168
- Kunen, K. Set theory, Elsevier, 1980
- Stanley, A. D-Spaces and a Dowker Space, thesis, Univ. Kansas 1997
Bibliographic Information
- William G. Fleissner
- Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
- Email: fleissne@math.ukans.edu
- Received by editor(s): March 8, 2000
- Received by editor(s) in revised form: June 6, 2000
- Published electronically: May 25, 2001
- Communicated by: Alan Dow
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 293-301
- MSC (2000): Primary 54D20; Secondary 54F05, 03E10
- DOI: https://doi.org/10.1090/S0002-9939-01-06026-9
- MathSciNet review: 1855648