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

Awartani, M. M.; Henderson, David W.

doi:10.1090/S0002-9939-1995-1307490-9

Compactifications of the ray with the arc as remainder admit no $n$-mean
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by M. M. Awartani and David W. Henderson PDF

Proc. Amer. Math. Soc. 123 (1995), 3213-3217 Request permission

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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