  In this paper we use the strength of the constraint method in combination
with a generalized Borsuk-Ulam type theorem and a cohomological intersection
lemma to show how one can obtain many new topological transversal theorems of
Tverberg type. In particular, we derive a topological generalized transversal
Van Kampen-Flores theorem and a topological transversal weak colored Tverberg
theorem.
