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Characterizing Continua by Disconnection Properties
Published online by Cambridge University Press: 20 November 2018
Abstract
We study Hausdorff continua in which every set of certain cardinality contains a subset which disconnects the space. We show that such continua are rim-finite. We give characterizations of this class among metric continua. As an application of our methods, we show that continua in which each countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.
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- Research Article
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- Copyright © Canadian Mathematical Society 1998