  Let C be convex, compact, with nonempty interior and h be Legendre with
domain C, continuous on C. We prove that h is Bregman if and only if it is
strictly convex on C and C is a polytope. This provides insights on sequential
convergence of many Bregman divergence based algorithm: abstract compatibility
conditions between Bregman and Euclidean topology may equivalently be replaced
by explicit conditions on h and C. This also emphasizes that a general
convergence theory for these methods (beyond polyhedral domains) would require
more refinements than Bregman's conditions.
