(ii) If K is closed, p satisfies (τ 2) and Ψ(x, .) is (k0 , K)-lsc, then Sk0 (x) is closed.Hence, if this is satisfied for all x ∈ X then ≤k0 is lower closed.(iii) If K is closed, p satisfies (τ 2) and Ψ(x, .) is (k0 , K)-lsca for all x ∈ X, then≤k0 is lower closed.To the best of our knowledge, all[r]