On the descriptive complexity of homogeneous continua

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 $c_0=\{(x_k)\in \mathbb R^ω: \lim x_k=0\}$ as a closed subset.

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