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A compact HL-space need not have a monolithic hyperspace
Author(s):
Henno
Brandsma;
Jan
van Mill
Journal:
Proc. Amer. Math. Soc.
126
(1998),
3407-3411.
MSC (1991):
Primary 54A20, 54B20, 54D30, 54G20
MathSciNet review:
1452794
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Abstract:
We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.
References:
- 1.
- A.V. Arhangel'ski[??]i, Topological Homogeneity. Topological Groups and their Continuous Images, Russian Math. Surveys 42 (1987), no. 2, 83-131.MR 89b:54004
- 2.
- M. Bell, The Hyperspace of a Compact Space I, Topology and its Applications 72 (1996), 39-46.MR 97j:54010
- 3.
- R. Engelking, General Topology, revised and completed ed., Sigma series in pure mathematics, vol. 6, Heldermann Verlag Berlin, 1989.MR 91c:54001
- 4.
- K. Kunen, A Compact L-space under CH, Topology and its Applications 12 (1981), 283-287.MR 82h:54065
- 5.
- K. Kunen and M. D\v{z}amonja, Measures on Compact HS spaces, Fundamenta Mathematicae 143 (1993), 41-54.MR 94h:54047
- 6.
- S. Negrepontis, Banach Spaces and Topology, Handbook of Set-Theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, 1984. MR 86i:46018
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Additional Information:
Henno
Brandsma
Affiliation:
Vrije Universiteit, Faculty of Mathematics and Computer Science, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Email:
hsbrand@cs.vu.nl
Jan
van Mill
Affiliation:
Vrije Universiteit, Faculty of Mathematics and Computer Science, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
Email:
vanmill@cs.vu.nl
DOI:
10.1090/S0002-9939-98-04374-3
PII:
S 0002-9939(98)04374-3
Keywords:
Hyperspaces,
monolithic,
compact spaces,
counterexamples
Received by editor(s):
July 30, 1996
Received by editor(s) in revised form:
March 19, 1997
Communicated by:
Alan Dow
Copyright of article:
Copyright
1998,
American Mathematical Society
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