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.
@article{bwmeta1.element.bwnjournal-article-cmv71i1p97bwm,
author = {K. Kawamura and E. Tymchatyn},
title = {Continua which admit no mean},
journal = {Colloquium Mathematicae},
volume = {70},
year = {1996},
pages = {97-105},
zbl = {0859.54022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p97bwm}
}
Kawamura, K.; Tymchatyn, E. Continua which admit no mean. Colloquium Mathematicae, Tome 70 (1996) pp. 97-105. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p97bwm/
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