# Continua which admit no mean

Colloquium Mathematicae (1996)

- Volume: 71, Issue: 1, page 97-105
- ISSN: 0010-1354

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topKawamura, K., and Tymchatyn, E.. "Continua which admit no mean." Colloquium Mathematicae 71.1 (1996): 97-105. <http://eudml.org/doc/210432>.

@article{Kawamura1996,

abstract = {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.},

author = {Kawamura, K., Tymchatyn, E.},

journal = {Colloquium Mathematicae},

keywords = {mean; pseudo-arc; unicoherent continuum},

language = {eng},

number = {1},

pages = {97-105},

title = {Continua which admit no mean},

url = {http://eudml.org/doc/210432},

volume = {71},

year = {1996},

}

TY - JOUR

AU - Kawamura, K.

AU - Tymchatyn, E.

TI - Continua which admit no mean

JO - Colloquium Mathematicae

PY - 1996

VL - 71

IS - 1

SP - 97

EP - 105

AB - 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.

LA - eng

KW - mean; pseudo-arc; unicoherent continuum

UR - http://eudml.org/doc/210432

ER -

## References

top- [Ba] P. Bacon, An acyclic continuum that admits no mean, Fund. Math. 67 (1970), 11-13. Zbl0192.60101
- [BeW] M. Bell and S. Watson, Not all dendroids have means, preprint. Zbl0860.54031
- [Bi1] R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742. Zbl0035.39103
- [Bi2] R. H. Bing, Snake-like continua, ibid. 18 (1951), 653-663. Zbl0043.16804
- [C] D. W. Curtis, A hyperspace retraction theorem for a class of half-line compactifications, Topology Proc. 11 (1986), 29-64. Zbl0638.54010
- [L] W. Lewis, Observations of the pseudo-arcs, ibid. 9 (1984), 329-337. Zbl0577.54038
- [M] J. Mioduszewski, On a quasi-ordering in the class of continuous mappings of a closed interval, Colloq. Math. 9 (1962), 233-240. Zbl0107.27603
- [O] L. G. Oversteegen, On products of confluent and weakly confluent mappings related to span, Houston J. Math. 12 (1986), 109-116. Zbl0638.54030
- [S] K. Sigmon, Acyclicity of compact means, Michigan Math. J. 16 (1969), 111-115. Zbl0179.51404

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