Local product structures on homogeneous continua

Abstract

Let X be a homogeneous continuum with H¹(X)≠0. A covering space X^∼ of X is constructed, as in [12] or [13], and it is shown that X^∼ is homeomorphic to the product of one of its components and a compact, totally disconnected homogeneous metric space. As an application, a new proof is given of Hagopian's theorem [6] that a homogeneous continuum whose only proper nondegenerate subcontinua are arcs must be a solenoid.