Let I be an ideal of a Noetherian ring R,and let N be a non-zero finitely generated R-module. In this paper, the main results are a relationship between the vanishing of the local cohomology modules H_I^i (N), and a comparison of the topologiesI
defined by the {(InN) ̅}n≥0 and {S((InN) ̅)}n≥0.
