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

Compactifications of the ray with the arc as remainder admit no $ n$-mean


Authors: M. M. Awartani and David W. Henderson
Journal: Proc. Amer. Math. Soc. 123 (1995), 3213-3217
MSC: Primary 54F15; Secondary 54D35
MathSciNet review: 1307490
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Abstract: An n-mean on X is a function $ F:{X^n} \to X$ which is idempotent and symmetric. In 1970 P. Bacon proved that the $ \sin (1/x)$ continuum admits no 2-mean. In this paper, it is proved that if X is any metric space which contains an open line one of whose boundary components in X is an arc, then X admits no n-mean, $ n \geq 2$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1307490-9
PII: S 0002-9939(1995)1307490-9
Keywords: Compactification of the ray, n-mean, mean, essential maps
Article copyright: © Copyright 1995 American Mathematical Society