Let R be a commutative Noetherian ring with non-zero identity, a and b ideals of R, and M a finitely generated R-module. In this paper, for non-negative integers n and j, we examine the question whether the support of Ext_R^j(R/b, H^n_a(M)) must be closed in Zariski topology, where H^n_a(M) is the n-th local cohomology module of M with respect to a. Several results giving an affirmative answer to this question are given.

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