1. CMB 2011 (vol 54 pp. 244)
|Homogeneous Suslinian Continua|
A continuum is said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum $X$ has the property that the set of points at which $X$ is connected im kleinen is dense in $X$. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.
Keywords:connected im kleinen, homogeneity, Suslinian, locally connected continuum
Categories:54F15, 54C05, 54F05, 54F50
2. CMB 2010 (vol 53 pp. 412)
|Einstein-Like Lorentz Metrics and Three-Dimensional Curvature Homogeneity of Order One|
We completely classify three-dimensional Lorentz manifolds, curvature homogeneous up to order one, equipped with Einstein-like metrics. New examples arise with respect to both homogeneous examples and three-dimensional Lorentz manifolds admitting a degenerate parallel null line field.
Keywords:Lorentz manifolds, curvature homogeneity, Einstein-like metrics
Categories:53C50, 53C20, 53C30