Hilbert cube [SEP] named after
Hilbert cube
In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology. Furthermore, many interesting topological spaces can be embedded in the Hilbert cube; that is, can be viewed as subspaces of the Hilbert cube (see below).
Definition.
The Hilbert cube is best defined as the topological product of the intervals [0, 1/"n"] for "n" = 1, 2, 3,
radius "e"  0 must go outside the cube in some dimension.
Any infinite-dimensional convex compact in formula_5 is homeomorphic to the Hilbert cube. The Hilbert cube is a convex set, whose span is the whole space, but whose interior is empty. This situation is impossible in finite dimensions. The tangent cone to the cube at the zero vector is the whole space.
Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable (and therefore T4) and second