The Cyclic Connectivity of Homogeneous Arcwise Connected Continua

David P. Bellamy
Lewis Lum, University of Portland

Abstract

A continuum is cyclicly connected provided each pair of its points lie together on some simple closed curve. In 1927, G. T. Whyburn proved that a locally connected plane continuum is cycicly connected if and only if it contains no separating points. This theorem was fundamental in his original treatment of cyclic element theory. Since then numerous authors have obtained extensions of Whybum's theorem. In this paper we characterize cyclic connectedness in the class of all Hausdorff continua.