  In this note we make several observations concerning symplectic fillings. In
particular we show that a (strongly or weakly) semi-fillable contact structure
is fillable and any filling embeds as a symplectic domain in a closed
symplectic manifold. We also relate properties of the open book decomposition
of a contact manifold to its possible fillings. These results are also useful
in proving property P for knots [P Kronheimer and T Mrowka, Geometry and
Topology, 8 (2004) 295-310, math.GT/0311489] and in showing the contact
Heegaard Floer invariant of a fillable contact structure does not vanish [P
Ozsvath and Z Szabo, Geometry and Topology, 8 (2004) 311-334, math.GT/0311496].
