  In this paper, we shall explore the Mosco convergence on regular subspaces of
one-dimensional irreducible and strongly local Dirichlet forms. We find that if
the characteristic sets of regular subspaces are convergent, then their
associated regular subspaces are convergent in sense of Mosco. Finally, we
shall show some examples to illustrate that the Mosco convergence does not
preserve any global properties of Dirichlet forms.
