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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
DOI: https://doi.org/10.1090/S0002-9939-1975-0375254-6
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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DOI: https://doi.org/10.1090/S0002-9939-1975-0375254-6
Keywords: Hausdorff continuum, hereditarily unicoherent, homogeneous, indecomposable, image of ordered compactum, metrizability
Article copyright: © Copyright 1975 American Mathematical Society