Characterizing Continua by Disconnection Properties

Characterizing Continua by Disconnection Properties

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 countab...

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Veröffentlicht in:Canadian mathematical bulletin 1998-09, Vol.41 (3), p.348-358
Hauptverfasser: Tymchatyn, E. D., Yang, Chang-Cheng
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0008-4395
1496-4287
DOI:10.4153/CMB-1998-047-0