Much of his early work focused on proofs surrounding Hilbert space and Hilbert cubes.
2.
Conversely, every Polish space is homeomorphic to a G ?-subset of the Hilbert cube.
3.
The Hilbert cube is obtained by taking a topological product of countably many copies of the unit interval.
4.
In the latter case, the resulting topology is the box topology; cylinder sets are never Hilbert cubes.
5.
Any such sequence belongs to the Hilbert space ! 2, so the Hilbert cube inherits a metric from there.
6.
The Hilbert cube is homeomorphic to the product of countably infinitely many copies of the unit interval [ 0, 1 ].
7.
Compact sets in Banach spaces may also carry natural measures : the Hilbert cube, for instance, carries the product Lebesgue measure.
8.
Every G ?-subset of the Hilbert cube is a Polish space, a topological space homeomorphic to a separable and complete metric space.
9.
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 ).
10.
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 ).
