Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Concerning upper semicontinuous decompositions of irreducible continua.


Authors: W. R. R. Transue, J. W. Hinrichsen and B. Fitzpatrick
Journal: Proc. Amer. Math. Soc. 30 (1971), 157-163
MSC: Primary 54.55
MathSciNet review: 0279774
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Abstract: Let $ \mathcal{K}$ denote the class of all compact metric continua K such that there exists a monotone mapping from a compact metric irreducible continuum M onto an arc such that each point inverse is homeomorphic to K. It is shown that no connected 1-polyhedron other than an arc is an element of $ \mathcal{K}$, but that $ \mathcal{K}$ contains certain locally connected continua.


References [Enhancements On Off] (What's this?)

  • [1] Eldon Dyer, Irreducibility of the sum of the elements of a continuous collection of continua, Duke Math. J. 20 (1953), 589–592. MR 0058198
  • [2] B. Knaster, Un continu irréductible à décomposition continue en tranches, Fund. Math. 25 (1935), 568-577.
  • [3] Casimir Kuratowski, Topologie. Vol. II, Troisième édition, corrigèe et complétée de deux appendices. Monografie Matematyczne, Tom 21, Państwowe Wydawnictwo Naukowe, Warsaw, 1961 (French). MR 0133124
  • [4] William S. Mahavier, Atomic mappings on irreducible Hausdorff continua, Fund. Math. 69 (1970), 147–151. MR 0283766
  • [5] R. L. Moore, Foundations of point set theory, Revised edition. American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279774-0
Keywords: Upper semicontinuous decomposition, irreducible metric continua, 1-polyhedra, simple closed curve
Article copyright: © Copyright 1971 American Mathematical Society