When using the functor Ω to pass from Top to Frm, all set-theoretic elements of a space are lost, but – using a fundamental idea of category theory – one can as well work on the function spaces. Indeed, any "point" "p""x": 1 → "X" in Top is mapped to a morphism Ω("p""x"): Ω("X") → Ω(1). The open set lattice of the one-element topological space Ω(1) is just (isomorphic to) the two-element locale 2 = { 0, 1 } with 0 < 1. After these observations it appears reasonable to define the set of points of a locale "L" to be the set of frame morphisms from "L" to 2. Yet, there is no guarantee that every point of the locale Ω("X") is in one-to-one correspondence to a point of the topological space "X" (consider again the indiscrete topology, for which the open set lattice has only one "point").