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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A compact HL-space need not have
a monolithic hyperspace


Authors: Henno Brandsma and 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 | References | Similar Articles | Additional Information

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.


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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: http://dx.doi.org/10.1090/S0002-9939-98-04374-3
PII: S 0002-9939(98)04374-3
Keywords: Hyperspaces, monolithic, compact spaces, counter\-examples
Received by editor(s): July 30, 1996
Received by editor(s) in revised form: March 19, 1997
Communicated by: Alan Dow
Article copyright: © Copyright 1998 American Mathematical Society