In mathematics, the Hilbert cube, named after David Hilbert, is a topological space that provides an instructive example of some ideas in topology.
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Conversely, every Polish space is homeomorphic to a Infinite-dimensional Lebesgue measure
Compact sets in Banach spaces may also carry natural measures: the Hilbert cube, for instance, carries the product Lebesgue measure.
Much of his early work focused on proofs surrounding Hilbert space and Hilbert cubes.
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Shape theory: Many shape invariants (Borsuk groups, Quigley inward and approaching groups) of a compact metric space can be obtained as exterior homotopy groups of the exterior space determined by the open neighborhoods of a compact metric space embedded in the Hilbert cube.