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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 disconnection properties, rim-finite continua, graphs
MSC Classifications: 54D05, 54F20, 54F50 show english descriptions Connected and locally connected spaces (general aspects)
unknown classification 54F20
Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
54D05 - Connected and locally connected spaces (general aspects)
54F20 - unknown classification 54F20
54F50 - Spaces of dimension $\leq 1$; curves, dendrites [See also 26A03]
 

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