Double algebraic genericity of universal forward-only harmonic functions on trees in the general case

It has been shown that the set of universal functions on trees contains a linear subspace except zero, dense in the space of forward-only harmonic functions. In this paper, we show that the set of universal functions contains two linear subspaces except zero, dense in the space of forward-only harmonic functions that intersect only at zero. We work in the most general case that has been studied so far, letting our functions take values over a topological vector space.