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SYNTAX: In checking theory, the domain of a head A is the set of nodes contained in Max(A) that are distinct from and do not contain A. EXAMPLE: in (i) the domain of X (a head) is the set of nodes UP, ZP, WP, YP, and H and whatever these categories dominate. XP1, XP2, X', X1 and X2 are not included in the domain of X, since each of these nodes contain X, and X is not distinct from X.

      /  \
     UP  XP2
       /  \
     ZP1    X'
    /\      /\
   /  \    /  \
  WP  ZP2  X1  YP
         /  \
        H   X2

Also see  Binding domain,  Governing domain,  

LIT. Chomsky, N. (1993)