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# Characterizing continua by disconnection properties

Published:1998-09-01
Printed: Sep 1998
• E. D. Tymchatyn
• Chang-Cheng Yang
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## 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.
 Keywords: disconnection properties, rim-finite continua, graphs
 MSC Classifications: 54D05 - Connected and locally connected spaces (general aspects) 54F20 - unknown classification 54F2054F50 - Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]