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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On homogeneous hereditarily unicoherent continua
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by G. R. Gordh PDF
Proc. Amer. Math. Soc. 51 (1975), 198-202 Request permission

Abstract:

Let $\mathfrak {M}$ denote the class of all hereditarily unicoherent Hausdorff continua in which each indecomposable subcontinuum is irreducible. It is shown that if the continuum $M$ in $\mathfrak {M}$ is decomposable, then the set of weak terminal points of $M$ is a nonempty, proper subset. The following generalization of a theorem of F. Burton Jones is an immediate corollary: if the continuum $M$ in $\mathfrak {M}$ is homogeneous, then $M$ is indecomposable. As an application, it is proved that if $X$ is a homogenous, hereditarily unicoherent Hausdorff continuum which is an image of an ordered compactum, then $X$ is an indecomposable metrizable continuum.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 51 (1975), 198-202
  • MSC: Primary 54F20
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0375254-6
  • MathSciNet review: 0375254