Descending closure operator

Ascending and descending closure operators induce strong deformation retractions of Z (P) onto A p P)). Here we give a short and self-contained inductive proof of the following stronger fact. 

Theorem 13.12. LetP be a poset, and let p he a descending closure operator. Then A P) collapses onto A(p P)). By symmetry, the same is true for an ascending closure operator. 

Consider the map ip P C[Pg.242]

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