0708-1300/the unit sphere in a Hilbert space is contractible
Let and define
For any and any define for and for . Observe that is continuous and gives the desired retraction to the point .
This proof only works in separable Hilbert spaces? Is the unit ball in a non-separable Hilbert space contractible?
The answer seems to be YES see Spheres in infinite-dimensional normed spaces are Lipschitz contractible