Domain (Syntax)

Domain is 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.

XP1 /\      /  \      UP  XP2 /\       /  \      ZP1    X'     /\      /\ / \    /  \   WP  ZP2  X1  YP           /\ / \         H   X2 Also see  Binding domain,  Governing domain, C-command.

Link
Utrecht Lexicon of Linguistics