= Inverse-limit solution of the reflexive domain equation
{title2=$D_\infty\cong[D_\infty\to D_\infty]$}
For $D_{n+1}=[D_n\to D_n]$ with recursively lifted <embedding-projection pairs>, form coherent sequences $x_n=p_nx_{n+1}$, ordered componentwise. Stage projections $P_n$ and embeddings $E_n$ satisfy $P_nE_n=\operatorname{id}$, $E_nP_n\uparrow\operatorname{id}$. A coherent family $f_n\in[D_n\to D_n]$ induces $f=\sup_nE_nf_nP_n$; conversely $f_n=P_nfE_n$. These constructions are inverse. Removing the initial coordinate of the coherent sequence identifies this function-space limit with the original domain limit.
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