  Based on general mathematical assumptions we give an independent, elementary
derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that
tree-level amplitudes of closed and open strings are related through the
single-valued map `sv'. This relation can be traced back to the underlying
moduli-space integrals over punctured Riemann surfaces of genus zero. The
sphere integrals $J$ in closed-string amplitudes and the disk integrals $Z$ in
open-string amplitudes are shown to obey $J = {\rm sv} \, Z$.
