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A necessary and sufficient condition for $ \beta X\backslash X$ to be an indecomposable continuum


Author: R. F. Dickman
Journal: Proc. Amer. Math. Soc. 33 (1972), 191-194
MSC: Primary 54D35
DOI: https://doi.org/10.1090/S0002-9939-1972-0295296-6
MathSciNet review: 0295296
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Abstract: In his dissertation, David Bellamy has shown that if $ I = [0,1)$, then $ \beta I\backslash I$ is an indecomposable continuum, and R. G. Woods, in his dissertation, obtained the same result and in addition showed that for $ m > 1,\beta {R^m}\backslash {R^m}$ is a decomposable continuum. In this note we give a necessary and sufficient condition for $ \beta X\backslash X$ to be an indecomposable continuum when X is a locally connected generalized continuum.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0295296-6
Keywords: Stone-Čech compactification, indecomposable continuum
Article copyright: © Copyright 1972 American Mathematical Society

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