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We shall prove that the Hilbert cube cannot be separated by a weakly infinitedimensional subset. As a corollary we obtain that the complement of a weaklyinfinite dimensional subset of the space of complete non negatively curvedmetrics is continuum connected. We can extend this result to the associatedmoduli space when the set removed is a Hausdorff space with Haver's property C.These results are refinements of theorems proven by Belegradek and Hu.

On separators of the space of complete non-negatively curved metrics on the plane