Geodesic
Characterizing Continua by Disconnection Properties
Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 348-358

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DOI

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.
DOI : 10.4153/CMB-1998-047-0
Mots-clés : 54D05, 54F20, 54F50, disconnection properties, rim-finite continua, graphs 
Tymchatyn, E. D.; Yang, Chang-Cheng. Characterizing Continua by Disconnection Properties. Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 348-358. doi: 10.4153/CMB-1998-047-0
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     title = {Characterizing {Continua} by {Disconnection} {Properties}},
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     pages = {348--358},
     year = {1998},
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     doi = {10.4153/CMB-1998-047-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-047-0/}
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