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Indecomposable Homogeneous Plane Continua are Hereditarily Indecomposable
Charles L. Hagopian
Transactions of the American Mathematical Society
Vol. 224, No. 2 (Dec., 1976), pp. 339-350
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1997480
Page Count: 12
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F. Burton Jones  proved that every decomposable homogeneous plane continuum is either a simple closed curve or a circle of homogeneous nonseparating plane continua. Recently the author  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 . At the Auburn Topology Conference in 1969, Professor Jones  outlined an argument for this theorem and stated that the details would be supplied later. However, those details have not appeared.
Transactions of the American Mathematical Society © 1976 American Mathematical Society