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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Indecomposable homogeneous plane continua are hereditarily indecomposable


Author: Charles L. Hagopian
Journal: Trans. Amer. Math. Soc. 224 (1976), 339-350
MSC: Primary 54F20
MathSciNet review: 0420572
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Abstract: F. Burton Jones [7] proved that every decomposable homogeneous plane continuum is either a simple closed curve or a circle of homogeneous nonseparating plane continua. Recently the author [5] showed that no subcontinuum of an indecomposable homogeneous plane continuum is hereditarily decomposable. It follows from these results that every homogeneous plane continuum that has a hereditarily decomposable subcontinuum is a simple closed curve. In this paper we prove that no subcontinuum of an indecomposable homogeneous plane continuum is decomposable. Consequently every homogeneous nonseparating plane continuum is hereditarily indecomposable. Parts of our proof follow one of R. H. Bing's arguments [2]. At the Auburn Topology Conference in 1969, Professor Jones [8] outlined an argument for this theorem and stated that the details would be supplied later. However, those details have not appeared.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0420572-1
PII: S 0002-9947(1976)0420572-1
Keywords: Homogeneity, indecomposable continua, nonseparating plane continua, hereditarily indecomposable continua, upper semicontinuous decomposition, pseudoarc
Article copyright: © Copyright 1976 American Mathematical Society