Continua which admit no mean

Volume 71 / 1996

K. Kawamura, E. Tymchatyn Colloquium Mathematicum 71 (1996), 97-105 DOI: 10.4064/cm-71-1-97-105


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.


  • K. Kawamura
  • E. Tymchatyn

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