Continua which admit no mean

• Autorzy: K. Kawamura , E. D. Tymchatyn
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

mean; pseudo-arc

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 71
• Numer: 1
• Strony: 97-105

Daty

wydano

1996

otrzymano

1995-04-05

poprawiono

1995-10-24

Twórcy

autor

K. Kawamura

• Institute of Mathematics, University of Tsukuba, Tsukuba-City, Ibaraki 305, Japan

autor

E. D. Tymchatyn

• Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5E6, Canada

Bibliografia

• [Ba] P. Bacon, An acyclic continuum that admits no mean, Fund. Math. 67 (1970), 11-13.
• [BeW] M. Bell and S. Watson, Not all dendroids have means, preprint.
• [Bi1] R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742.
• [Bi2] R. H. Bing, Snake-like continua, ibid. 18 (1951), 653-663.
• [C] D. W. Curtis, A hyperspace retraction theorem for a class of half-line compactifications, Topology Proc. 11 (1986), 29-64.
• [L] W. Lewis, Observations of the pseudo-arcs, ibid. 9 (1984), 329-337.
• [M] J. Mioduszewski, On a quasi-ordering in the class of continuous mappings of a closed interval, Colloq. Math. 9 (1962), 233-240.
• [O] L. G. Oversteegen, On products of confluent and weakly confluent mappings related to span, Houston J. Math. 12 (1986), 109-116.
• [S] K. Sigmon, Acyclicity of compact means, Michigan Math. J. 16 (1969), 111-115.