Means on chainable continua

Author:
Mirosław Sobolewski

Journal:
Proc. Amer. Math. Soc. **136** (2008), 3701-3707

MSC (2000):
Primary 54F15

DOI:
https://doi.org/10.1090/S0002-9939-08-09414-8

Published electronically:
May 15, 2008

MathSciNet review:
2415058

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Abstract | References | Similar Articles | Additional Information

Abstract: By a mean on a space we understand a mapping such that and for . A chainable continuum is a metric compact connected space which admits an - mapping onto the interval for every number . We show that every chainable continuum that admits a mean is homeomorphic to the interval. In this way we answer a question by P. Bacon. We answer some other questions concerning means as well.

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Additional Information

**Mirosław Sobolewski**

Affiliation:
Instytut Matematyki, Banacha 2, Warszawa 02-097, Poland

Email:
msobol@mimuw.edu.pl

DOI:
https://doi.org/10.1090/S0002-9939-08-09414-8

Keywords:
Continuum,
chainable,
mean

Received by editor(s):
September 22, 2006

Received by editor(s) in revised form:
August 14, 2007

Published electronically:
May 15, 2008

Communicated by:
Alexander N. Dranishnikov

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.