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

 

Vietoris continuous selections and disconnectedness-like properties


Authors: Valentin Gutev and Tsugunori Nogura
Journal: Proc. Amer. Math. Soc. 129 (2001), 2809-2815
MSC (2000): Primary 54C65, 54B20, 54F45
Published electronically: February 9, 2001
MathSciNet review: 1838807
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Abstract:

Suppose that $X$ is a Hausdorff space such that its Vietoris hyperspace $({\mathcal{F}}(X),\tau _{V})$ has a continuous selection. Do disconnectedness-like properties of $X$ depend on the variety of continuous selections for $({\mathcal{F}}(X),\tau _{V})$ and vice versa? In general, the answer is ``yes'' and, in some particular situations, we were also able to set proper characterizations.


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Additional Information

Valentin Gutev
Affiliation: School of Mathematical and Statistical Sciences, Faculty of Science, University of Natal, King George V Avenue, Durban 4041, South Africa
Email: gutev@sci.und.ac.za

Tsugunori Nogura
Affiliation: Department of Mathematics, Faculty of Science, Ehime University, Matsuyama, 790 Japan
Email: nogura@ehimegw.dpc.ehime-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05883-X
PII: S 0002-9939(01)05883-X
Keywords: Selections, hyperspaces, zero-dimensionality
Received by editor(s): November 17, 1999
Received by editor(s) in revised form: January 17, 2000
Published electronically: February 9, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society