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Monotonically countably paracompact, collectionwise Hausdorff spaces and measurable cardinals
Authors:
Chris Good and Robin W. Knight
Journal:
Proc. Amer. Math. Soc. 134 (2006), 591-597
MSC (2000):
Primary 54C10, 54D15, 54D20, 54E20, 54E30
Posted:
June 14, 2005
MathSciNet review:
2176028
Full-text PDF Free Access
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Additional Information
Abstract: We show that, if an MCP (monotonically countably paracompact) space fails to be collectionwise Hausdorff, then there is a measurable cardinal and that, if there are two measurable cardinals, then there is an MCP space that fails to be collectionwise Hausdorff.
References
- 1.
D. Burke,
 and first countable, countably paracompact spaces, Proc. Amer. Math. Soc., 92 (1984), 455-460. MR 0759673 (85h:54032)
- 2.
W.W. Comfort, and S. Negrepontis, The theory of ultrafilters (Springer-Verlag, Berlin, 1974). MR 0396267 (53:135)
- 3.
C. Good, R. W. Knight and I. S. Stares, Monotone Countable Paracompactness, Topol. Appl., 101 (2000), 281-298. MR 1733809 (2000k:54024)
- 4.
C. Good, D. W. McIntyre, W. S. Watson, Measurable cardinals and finite intervals between regular topologies, Topol. Appl., 123 (2002), 429-441. MR 1924043 (2003h:54001)
- 5.
C. Good and G. Ying, A note on monotone countable paracompactness, Comment. Math. Univ. Carolinae, 42 (2001), 771-778. MR 1883385 (2003a:54027)
- 6.
R. Engelking, General Topology, (Heldermann Verlag, Berlin 1989). MR 1039321 (91c:54001)
- 7.
W. G. Fleissner, The normal Moore space conjecture and large cardinals, in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan, eds. (North-Holland, Amsterdam, 1984). MR 0776635 (86m:54023)
- 8.
G. Gruenhage, Generalized metric spaces, in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan, eds. (North-Holland, Amsterdam, 1984). MR 0776629 (86h:54038)
- 9.
R. E. Hodel, Spaces defined by sequences of open covers which guarantee that certian sequences have cluster points, Proceedings of the University of Houston Point Set Topology Conference (Houston, Tex., 1971), (1971), 105-114. MR 0407810 (53:11580)
- 10.
K. Kunen, Set Theory, An Introduction to Independence Proofs, North Holland, Amsterdam (1983). MR 0756630 (85e:03003)
- 11.
A. Lévy and R. M. Solovay, Measurable cardinals and the continuum hypothesis, Israel J. Math., 5 (1967), 234-248. MR 0224458 (37:57)
- 12.
T. C. Przymusinski, Products of normal spaces, in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan, eds. (North-Holland, Amsterdam, 1984). MR 0776637 (86c:54007)
- 13.
M. E. Rudin, Dowker spaces, in Handbook of set-theoretic topology, K. Kunen and J. E. Vaughan, eds. (North-Holland, Amsterdam, 1984). MR 0776636 (86c:54018)
- 14.
W. S. Watson, Separation in countably paracompact spaces, Trans. Amer. Math. Soc., 290 (1985), 831-842. MR 0792831 (87b:54016)
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Additional Information
Chris Good
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT, United Kingdom
Email:
c.good@bham.ac.uk
Robin W. Knight
Affiliation:
Mathematical Institute, University of Oxford, 24-29 St Giles', Oxford OX1 3LB, United Kingdom
Email:
knight@maths.ox.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-07965-7
PII:
S 0002-9939(05)07965-7
Keywords:
Monotone countable paracompactness,
MCP,
collectionwise Hausdorff,
measurable cardinals
Received by editor(s):
July 30, 2003
Received by editor(s) in revised form:
September 9, 2004
Posted:
June 14, 2005
Communicated by:
Alan Dow
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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