1. CMB 1998 (vol 41 pp. 348)
|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 countably infinite set disconnects are generalized graphs. This extends a result of Nadler for metric continua.
Keywords:disconnection properties, rim-finite continua, graphs
Categories:54D05, 54F20, 54F50