I was wondering if there is such a thing like a Hilbertian affine space. I've seen the definition of an Euclidian affine space, which is:
An affine space (A, V, φ) is an Euclidean affine space if the vector space V is an Euclidean vector space.
Thus, it makes me think that an affine space would be a Hilbertian affine space if the vector space V is a Hilbertian vector space. Is this right? or is there any incompatibility between both spaces (affine and Hilbert spaces)?