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Proceedings of the American Mathematical Society
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 | References | Similar Articles | Additional Information

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?)

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  • [2] B. Knaster, Un continu irréductible à décomposition continue en tranches, Fund. Math. 25 (1935), 568-577.
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279774-0
PII: S 0002-9939(1971)0279774-0
Keywords: Upper semicontinuous decomposition, irreducible metric continua, 1-polyhedra, simple closed curve
Article copyright: © Copyright 1971 American Mathematical Society



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