Abstract
All subsets P of an irreducible affine root system R such that P and R⧹ P are closed under addition of roots are classified. It is shown that if 0: R → R′ is a bijection of root systems such that 0 and 0 −1 preserve closed sets and the irreducible components of R and R′ are affine or finite with at most one irreducible component of type A i then θ is an isomorphism of root systems.
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