On the descriptive complexity of homogeneous continua

Abstract

It is shown that the family of all homogeneous continua in the hyperspace of all subcontinua of any finite-dimensional Euclidean cube or the Hilbert cube is an analytic subspace of the hyperspace which contains a topological copy of the linear space $c_0=\{(x_k)\in {\mathbb{R}}^{\omega }:\lim x_k=0\}$ as a closed subset.