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There are many Kunen compact L-spaces
Author(s):
Henno
Brandsma;
Jan
van Mill
Journal:
Proc. Amer. Math. Soc.
128
(2000),
2165-2170.
MSC (1991):
Primary 54D35
Posted:
November 29, 1999
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Abstract:
We prove that under CH there are  non-homeomorphic Kunen compact L-spaces. Moreover there exist models of ZFC that have  many non-homeomorphic Kunen spaces.
References:
- 1.
- M. Bell, The Hyperspace of a Compact Space I, Topology and its Applications 72 (1996), 39-46. MR 97j:54010
- 2.
- H. Brandsma and J. van Mill, A Compact HL Space need not have a Monolithic Hyperspace, Proceedings of the AMS 126 (1998), 3407-3411. MR 99a:54007
- 3.
- H. Brandsma and J. van Mill, Every Kunen-like L-space has a non-monolithic hyperspace, Proceedings of the 12th Summer Conference on General Topology and its Applications, 1997.
- 4.
- K. Kunen, Set theory. An introduction to independence proofs, Studies in Logic and the foundations of Mathematics, vol. 102, North-Holland, Amsterdam, 1980. MR 82f:03001
- 5.
- K. Kunen, A Compact L-space under CH, Topology and its Applications 12 (1981), 283-287. MR 82h:54065
- 6.
- K. Kunen and J. van Mill, Measures on Corson Compact Spaces, Fundamenta Mathematicae 147 (1995), 61-72. MR 96c:54040
- 7.
- E. V. \v{S}\v{c}epin, Functors and uncountable degrees of compacta, Uspekhi Mat. Nauk 36 (1981), no. 3(219), 3-62, 255. MR 82k:54012
- 8.
- Z. Semadeni, Banach spaces of continuous functions, volume I, Monografie Matematyczne, vol. 55, PWN - Polish scientific publishers, Warsaw, 1971. 45:5730
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Additional Information:
Henno
Brandsma
Affiliation:
Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081~HV Amsterdam, the Netherlands
Email:
hsbrand@cs.vu.nl
Jan
van Mill
Affiliation:
Faculteit Wiskunde en Informatica, Vrije Universiteit, De Boelelaan 1081a, 1081~HV Amsterdam, the Netherlands
Email:
vanmill@cs.vu.nl
DOI:
10.1090/S0002-9939-99-05186-2
PII:
S 0002-9939(99)05186-2
Keywords:
CH,
L-space,
measure
Received by editor(s):
March 20, 1998
Received by editor(s) in revised form:
August 5, 1998.
Posted:
November 29, 1999
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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