# Hilbert cube

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The subspace of the Hilbert space consisting of all the points for which , . The Hilbert cube is a compactum and is topologically equivalent (homeomorphic) to the Tikhonov product of a countable system of intervals, i.e. to the Tikhonov cube . It is a universal space in the class of metric spaces with a countable base (Urysohn's metrization theorem).