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Baire spaces, Tychonoff powers and the Vietoris topology
Author(s):
Jiling
Cao;
A.
H.
Tomita
Journal:
Proc. Amer. Math. Soc.
135
(2007),
1565-1573.
MSC (2000):
Primary 54E52;
Secondary 54B10, 54B20, 91A05
Posted:
January 4, 2007
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Abstract:
In this paper, we show that if the Tychonoff power  of a quasi-regular space  is Baire, then its Vietoris hyperspace  is also Baire. We also provide two examples to show (i) the converse of this result does not hold in general, and (ii) the Baireness of finite powers of a space is insufficient to guarantee the Baireness of its hyperspace.
References:
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Additional Information:
Jiling
Cao
Affiliation:
School of Mathematical Sciences, Auckland University of Technology, Private Bag 92006, Auckland 1020, New Zealand
Email:
jiling.cao@aut.ac.nz
A.
H.
Tomita
Affiliation:
Departamento de Matemática, Institute of Mathematics and Statistics, University of São Paulo, 05315 São Paulo, Brazil
Email:
tomita@ime.usp.br
DOI:
10.1090/S0002-9939-07-08855-7
PII:
S 0002-9939(07)08855-7
Keywords:
Baire space,
Choquet game,
Tychonoff power,
Vietoris topology.
Received by editor(s):
February 13, 2006
Posted:
January 4, 2007
Additional Notes:
The first-named author acknowledges the support from a Marsden Fund grant, UOA0422, administrated by the Royal Society of New Zealand. The second-named author wishes to thank the financial support from the Foundation of Research, Science and Technology of New Zealand and the warm hospitality of his host during his visit to the University of Auckland in July 2005.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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