Before defining the required topology on pt("X"), it is worthwhile to clarify the concept of a point of a locale further. The perspective motivated above suggests to consider a point of a locale "L" as a frame morphism "p" from "L" to 2. But these morphisms are characterized equivalently by the inverse images of the two elements of 2. From the properties of frame morphisms, one can derive that "p" −1(0) is a lower set (since "p" is monotone), which contains a greatest element "a""p" = V "p" −1(0) (since "p" preserves arbitrary suprema). In addition, the principal ideal "p" −1(0) is a prime ideal since "p" preserves finite infima and thus the principal "a""p" is a meet-prime element. Now the set-inverse of "p" −1(0) given by "p" −1(1) is a completely prime filter because "p" −1(0) is a principal prime ideal. It turns out that all of these descriptions uniquely determine the initial frame morphism. We sum up: