In 1928, at the International Mathematical Congress held in Bologna (Italy), Frigyes Riesz introduced the notion of a vector lattice on function spaces and discussed linear operators that preserve the join operation, nowadays known as Riesz homomorphisms. In this survey, we review the behavior of some nonlinear join-preserving Riesz space-valued functions, and we show how existing addition-dependent results can be proved in these environments mutatis mutandis.

(Readers are referred to papers [1, 2, 3, 4, 6, 7, 8, 9, 10, 5] for more information.)