1. CMB 2005 (vol 48 pp. 195)
|On Suslinian Continua |
A continuum is said to be Suslinian if it does not contain uncountably many mutually exclusive nondegenerate subcontinua. We prove that Suslinian continua are perfectly normal and rim-metrizable. Locally connected Suslinian continua have weight at most $\omega_1$ and under appropriate set-theoretic conditions are metrizable. Non-separable locally connected Suslinian continua are rim-finite on some open set.
Keywords:Suslinian continuum, Souslin line, locally connected, rim-metrizable,, perfectly normal, rim-finite
Categories:54F15, 54D15, 54F50
2. 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