# Hilbert cube

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The subspace of the Hilbert space $l_2$ consisting of all the points $x=(x_1,x_2,\ldots)$ for which $0\leq x_n\leq(1/2)^n$, $n=1,2,\ldots$. 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 $I^{\aleph_0}$. It is a universal space in the class of metric spaces with a countable base (Urysohn's metrization theorem).