On 1/2-homogeneous continua

Abstract

A continuum is 1/2-homogeneous provided there are exactly two orbits for the action of the group of homeomorphisms of the continuum onto itself. In this paper we study some relations between 1/2-homogeneous continua and their set of cut points. We also prove that if X is a hereditarily decomposable continuum whose proper, nondegenerate subcontinua are arc-like, then X is 1/2-homogeneous if and only if X is an arc. Suitable examples and counterexamples are given. (C) 2005 Elsevier B.V. All rights reserved.