On the continua which are Cantor homogeneous or arcwise homogeneous

Curvature Homogeneous Pseudo-riemannian Manifolds Which Are Not Locally Homogeneous

We construct a family of balanced signature pseudo-Riemannian manifolds, which arise as hypersurfaces in flat space, that are curvature homogeneous, that are modeled on a symmetric space, and that are not locally homogeneous.

SOME THEOREMS ON n-HOMOGENEOUS CONTINUA

Certain Homogeneous Unicoherent Indecomposable Continua

A simple closed curve is the simplest example of a compact, nondegenerate, homogeneous continuum. If a bounded, nondegenerate, homogeneous plane continuum has any local connectedness property, even of the weakest sort, it is known to be a simple closed curve [l, 2, 3].1 The recent discovery of a bounded, nondegenerate, homogenous plane continuum which does not separate the plane [4, 5] has give...

Simply Connected Homogeneous Continua Are Not Separated by Arcs

We show that locally connected, simply connected homogeneous continua are not separated by arcs. We ask several questions about homogeneous continua which are inspired by analogous questions in geometric group theory.

Optimal Quantization for Dyadic Homogeneous Cantor Distributions

For a large class of dyadic homogeneous Cantor distributions in R, which are not necessarily self-similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non-existence of the quantization coefficient. The class contains all self-similar dyadic Cantor distributions, with contraction factor less than or equal to 1 3 . For...