  We construct an explicit solution of the Seiberg-Witten map for a linear
gauge field on the non-commutative plane. We observe that this solution as well
as the solution for a constant curvature diverge when the non-commutativity
parameter theta reaches certain event horizon in the theta-space. This implies
that an ordinary Yang-Mills theory can be continuously deformed by the
Seiberg-Witten map into a non-commutative theory only within one connected
component of the theta-space.
