I wonder if an affine transformation between real affine spaces (defined as in Characterisation of affine transformations ) preserves convexity.
I recall that a subset of a real affine space is convex if, for every two its points A and B, it contains the point A+k(B-A) for every k in [0,1] (real line interval). A function between affine spaces preserves convexity if the image of every convex subset of the domain is convex (in the codomain).