Affine semigroups
Haskell Cohen, H. S. Collins · Transactions of the American Mathematical Society · 1959
In what follows X and Y are topological vector spaces (Hausdorff) over the reals, and 5 and T are subsets of X and Y respectively.When 5 and T are convex, a mapping/: S-^T is said to be affine if/ preserves convex combinations: x, y(ES, O^agl impliesf(ax + (l-a)y) = af(x) + (1 -a)f(y).It is easy to verify (and well known) that if / is affine, then / preserves more general combinations: /(^2l= i ctiXi) = 22l=i a'f(xi) whenever X\, ■ ■ -,xn G S,