Finally, one can verify that for every space "X", Ω("X") is spatial and for every locale "L", pt("L") is sober. Hence, it follows that the above adjunction of Top and Loc restricts to an equivalence of the full subcategories Sob of sober spaces and SLoc of spatial locales. This main result is completed by the observation that for the functor pt o Ω, sending each space to the points of its open set lattice is left adjoint to the inclusion functor from Sob to Top. For a space "X", pt(Ω("X")) is called its soberification. The case of the functor Ω o pt is symmetric but a special name for this operation is not commonly used.