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

 

Continuous selections and $C$-spaces


Authors: Valentin Gutev and Vesko Valov
Journal: Proc. Amer. Math. Soc. 130 (2002), 233-242
MSC (2000): Primary 54C60, 54C65, 55M10
Published electronically: May 22, 2001
MathSciNet review: 1855641
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Abstract:

A characterization of paracompact $C$-spaces via continuous selections avoiding $Z_\infty$-sets is given. The result is applied to prove a countable sum theorem for paracompact $C$-spaces, and to obtain a new partial solution of a question raised by E. Michael.


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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@nu.ac.za

Vesko Valov
Affiliation: Department of Mathematics, Nipissing University, 100 College Drive, P. O. Box 5002, North Bay, Ontario, Canada P1B 8L7
Email: veskov@unipissing.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05995-0
PII: S 0002-9939(01)05995-0
Keywords: Continuous selection, $C$-space, $Z_\infty$-set
Received by editor(s): November 17, 1999
Received by editor(s) in revised form: May 9, 2000
Published electronically: May 22, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society