The conditions under which a component (e.g., solvent) chemical potential in an n-component system passes an extremum during movement along isothermal-isobaric monovariant (n-1)-phase solubility equilibrium lines and three-phase solubility equilibrium hypersurfaces are considered. For the overwhelming majority of systems, solvent chemical potential extrema are maxima. From the point of view of topological isomorphism, these solvent chemical potential extrema are analogues of van Rain melting-point diagram points.