A necessary and sufficient condition for 𝛽𝑋\𝑋 to be an indecomposable continuum

Dickman, R. F.

doi:10.1090/S0002-9939-1972-0295296-6

A necessary and sufficient condition for $\beta X\backslash X$ to be an indecomposable continuum
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Proc. Amer. Math. Soc. 33 (1972), 191-194 Request permission

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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