It is shown that the locations of the characteristic topological features in the average local electrostatic potential defined by the ratio of the electrostatic potential V(r) and the spherically averaged electron density rho(r) can be identified with the intershell boundaries in the lanthanoid atoms and their tripositive ions. Numerical tests carried out using the nonrelativistic numerical Hartree-Fock densities establish the validity of the Politzer-Parr partitioning of the core-valence region for the heavier atoms and ions.