  We study continuous (strongly) minimal cut generating functions for the model
where all variables are integer. We consider both the original Gomory-Johnson
setting as well as a recent extension by Cornu\'ejols and Y{\i}ld{\i}z. We show
that for any continuous minimal or strongly minimal cut generating function,
there exists an extreme cut generating function that approximates the
(strongly) minimal function as closely as desired. In other words, the extreme
functions are "dense" in the set of continuous (strongly) minimal functions.
