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In this paper, on the family O(Y ) of all open subsets of a space Y (actually on a complete lattice) we define the so called strong v-Scott topology, denoted by τ8v,  where v is an infinite cardinal. This topology defines on the set C(Y,Z) of all continuous functions on the space Y to a space Z a topology τ8v. The topology τ8v, is always larger than or equal to the strong Isbell topology. We study the topology τ8v in the case where Y is a locally v-bounded space.