Homogeneous continua in Euclidean $(n+1)$-space which contain an $n$-cube are locally connected

More Monotone Open Homogeneous Locally Connected Plane Continua

This paper constructs a continuous decomposition of the Sierpiński curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpiński curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpiński curve and identifying two points on the boundary of one of its complemen...

Graphs which are locally a cube

Let (e,, e2, e3, e4) be the standard basis of R4. The 24-ceI& is a 4-dimensional regular polytope whose vertices are the 24 vectors *q =te, (i # i) of R4, two vertices being adjacent iff the angle between the corresponding vectors is 60’. It is well known [2] and easy to check that the l-skeleton (i.e. the graph consisting of the vertices and edges) of this polytope has the following property: ...

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.

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.

Locally-finite connected-homogeneous digraphs