For a poset P, let σ(P) and Γ(P) respectively denote the lattice of its Scott open subsets closed ordered by inclusion, set ΣP=(P,σ(P)). In this paper, we discuss lower Vietoris topology on give some sufficient conditions to make two topologies equal. We build an adjunction between σ(Γ(P)) prove that ΣP is core-compact iff ΣΓ(P) sober, locally compact σ(Γ(P))=υ(Γ(P)) (the topology). This answer...