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

DOI:
https://doi.org/10.1090/S0002-9939-01-05883-X

Published electronically:
February 9, 2001

MathSciNet review:
1838807

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Suppose that is a Hausdorff space such that its Vietoris hyperspace has a continuous selection. Do disconnectedness-like properties of depend on the variety of continuous selections for 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:
https://doi.org/10.1090/S0002-9939-01-05883-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