Geodesic
Continua which admit no mean
Colloquium Mathematicum, Tome 71 (1996) no. 1, pp. 97-105
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A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.
DOI : 10.4064/cm-71-1-97-105
Keywords: mean, pseudo-arc 
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K. Kawamura; E. Tymchatyn. Continua which admit no mean. Colloquium Mathematicum, Tome 71 (1996) no. 1, pp. 97-105. doi: 10.4064/cm-71-1-97-105

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