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Proceedings of the American Mathematical Society

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



On homogeneous hereditarily unicoherent continua

Author: G. R. Gordh
Journal: Proc. Amer. Math. Soc. 51 (1975), 198-202
MSC: Primary 54F20
MathSciNet review: 0375254
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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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Keywords: Hausdorff continuum, hereditarily unicoherent, homogeneous, indecomposable, image of ordered compactum, metrizability
Article copyright: © Copyright 1975 American Mathematical Society