  In this paper, we test the weak cosmic censorship conjecture (WCCC) for n >=
4 dimensional nearly extremal RN-AdS black holes with non-trivial topologies,
namely plane and hyperbola, using the new version of gedanken experiment
proposed by Sorce and Wald. Provided that the non-electromagnetic part of the
stress tensor of matter fields satisfies the null energy condition and the
linear stability condition holds, we find that the black holes cannot be
overcharged under the second-order perturbation approximation, which includes
the self-force and finite-size effects. As a result, we conclude that the
violation of Hubeny type never occurs and the WCCC holds for the topological
RN-AdS black hole.
