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==Theorem==
Let $X$ be a nondegenerate [[continuum]]. Then the following are equivalent:
# [[hyperspace|$2^X$]] is [[homogeneous]],
# $X$ is a [[Peano continuum]],
# $2^X$ is [[homeomorphic]] to the [[Hilbert cube]].

==Proof==

==References==

[[Category:Theorem]]
[[Category:Unproven]]

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