The categories LTop0 and L-Sob as epireflective hulls

We show that the category \(L\)-\(\mathbf{Top}_{0}\) of \(T_{0}\)-\(L\)-topological spaces is the epireflective hull of Sierpinski \(L\)-topological space in the category \(L\)-\(\mathbf{Top}\) of \(L\)-topological spaces and the category \(L\)-\(\mathbf{Sob}\) of sober \(L\)-topological spaces is the epireflective hull of Sierpinski \(L\)-topological space in the category \(L\)-\(\mathbf{Top}_{0}\).