 The hierarchy of all the function spaces \(D_n\) may be accumulated together. A standard construction in model theory is to form the disjoint union of structures. (Disjointness can always be guaranteed by indexing the carrier sets of the structures.) Scott defined \(D_\infty\) to be the disjoint union of the function spaces \(D_n\), for all \(n\), except that the extremal elements are “glued together.” (More formally, the top elements and the bottom elements of the function spaces, respectively, are identified with each other.) \(D_\infty\) is a complete lattice, and by Tarski’s fixed point theorem, a continuous function that maps  \(D_\infty\) into \(D_\infty\) has a fixed point, which implies that \(D _\infty\) is isomorphic to \(D_\infty\rightarrow D_\infty\).