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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Indecomposable homogeneous plane continua are hereditarily indecomposable
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by Charles L. Hagopian PDF
Trans. Amer. Math. Soc. 224 (1976), 339-350 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 224 (1976), 339-350
  • MSC: Primary 54F20
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0420572-1
  • MathSciNet review: 0420572