Characterizing Continua by Disconnection Properties

Tymchatyn, E. D. ; Yang, Chang-Cheng

Canadian mathematical bulletin, Tome 41 (1998) no. 3, pp. 348-358

Résumé

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.

Détail

DOI : 10.4153/CMB-1998-047-0

Mots-clés : 54D05, 54F20, 54F50, disconnection properties, rim-finite continua, graphs

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