  We prove that, under a simple condition on the cohomology ring, every closed
4-manifold has mod 2 Seiberg-Witten simple type. This result shows that there
exists a large class of topological 4-manifolds such that all smooth structures
have mod 2 simple type, and yet some have non-vanishing (mod 2) Seiberg-Witten
invariants. As corollaries, we obtain adjunction inequalities and show that,
under a mild topological condition, every geometrically simply connected closed
4-manifold has the vanishing mod 2 Seiberg-Witten invariant for at least one
orientation.
