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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F15, 54D35

Retrieve articles in all journals with MSC: 54F15, 54D35

Additional Information

Keywords: Compactification of the ray, n-mean, mean, essential maps
Article copyright: © Copyright 1995 American Mathematical Society