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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.

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Keywords: Upper semicontinuous decomposition, irreducible metric continua, 1-polyhedra, simple closed curve
Article copyright: © Copyright 1971 American Mathematical Society

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