Let I be an ideal of a Noetherian ring R. The purpose of this paper is
to study the relationship between the vanishing of the local cohomolo
gy modules H-I(i)(R), and the comparison of the topologies defined by
the I-adic {I-n}(n) (greater than or equal to) (0), the symbolic {I-(n
)} (n) (greater than or equal to) (0) and the integral filtration {($)
over bar I-$ over bar n}(n) (greater than or equal to) (0).