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)?


closed as unclear what you're asking by Delta-u, David Hill, max_zorn, Adrian Keister, Thomas Shelby Feb 28 at 2:05

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  • $\begingroup$ I don't know what you mean by "Hilbertian space" $\endgroup$ – David Hill Feb 27 at 18:27