Symmetry among subcontinua with finite boundary in a homogeneous continuum.

摘要

Continua are sometimes defined as compact, connected metric spaces. In this thesis, we use the more general definition of a continuum as a compact, connected, Hausdorff topological space. An n-pod is defined to be a subcontinuum of a topological space whose boundary contains exactly n points, where n is an integer greater than 1. Preliminary results of general topological spaces, continua, homogeneous continua, and n-pods are developed to provide access to the main result. Finally, a symmetry is established among n-pods by verifying that for each n-pod in H in a homogeneous continuum, there exists another n-pod containing the same boundary which is symmetrical to H relative to the boundary of H.