Continua which admit no mean

K. Kawamura; E. Tymchatyn

Colloquium Mathematicae (1996)

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

Abstract

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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.

How to cite

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Kawamura, 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

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  1. [Ba] P. Bacon, An acyclic continuum that admits no mean, Fund. Math. 67 (1970), 11-13. Zbl0192.60101
  2. [BeW] M. Bell and S. Watson, Not all dendroids have means, preprint. Zbl0860.54031
  3. [Bi1] R. H. Bing, A homogeneous indecomposable plane continuum, Duke Math. J. 15 (1948), 729-742. Zbl0035.39103
  4. [Bi2] R. H. Bing, Snake-like continua, ibid. 18 (1951), 653-663. Zbl0043.16804
  5. [C] D. W. Curtis, A hyperspace retraction theorem for a class of half-line compactifications, Topology Proc. 11 (1986), 29-64. Zbl0638.54010
  6. [L] W. Lewis, Observations of the pseudo-arcs, ibid. 9 (1984), 329-337. Zbl0577.54038
  7. [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
  8. [O] L. G. Oversteegen, On products of confluent and weakly confluent mappings related to span, Houston J. Math. 12 (1986), 109-116. Zbl0638.54030
  9. [S] K. Sigmon, Acyclicity of compact means, Michigan Math. J. 16 (1969), 111-115. Zbl0179.51404

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