Finitely Cyclic Homogeneous Continua

On Finitely Equivalent Continua

A continuum means a compact connected metric space. For a positive integer n, a continuum X is said to be n-equivalent provided that X contains exactlyn topologically distinct subcontinua. A continuumX is said to be hereditarily n-equivalent provided that each nondegenerate subcontinuum of X is n-equivalent. If there exists a positive integer n such that X is n-equivalent, then X is said to be ...

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...

SOME THEOREMS ON n-HOMOGENEOUS CONTINUA

A Complete Classification of Homogeneous Plane Continua

We show that the only compact and connected subsets (i.e. continua) X of the plane R2 which contain more than one point and are homogeneous, in the sense that the group of homeomorphisms of X acts transitively on X, are, up to homeomorphism, the circle S1, the pseudo-arc, and the circle of pseudo-arcs. These latter two spaces are fractal-like objects which do not contain any arcs. It follows th...

Locally homogeneous finitely nondegenerate CR-manifolds

In several areas of mathematics, homogeneous spaces are fundamental objects as they often serve as models for more general objects: Various examples from differential geometry (Riemannian symmetric spaces, principal bundles) and topology (geometric 3-manifolds), to algebraic and complex geometry (uniformization theorems, flag manifolds) etc. underline the importance of spaces, furnished with a ...