  The theta--fan F_theta is the quotient space obtained by identifying the
non--isolated points of the product theta \times (omega+1) with a single point
\infty. (Here, theta has the discrete topology and omega+1 has the order
topology.)
  We define several notions of forcing that allow us to manipulate the
tightness t of products of fans. Some consequences include: t (F_theta \times
F_omega) = theta does not imply the existence of a (theta,omega)--gap, new
examples of first countable <theta--collectionwise Hausdorff (cwH) spaces that
are not \leq theta--cwH for singular cardinals theta, and for cardinals lambda
\leq theta with cf(theta) \geq omega_1 and lambda regular, a first countable
<theta--cwH not \leq theta--cwH space that can be made cwH by removing a closed
discrete set of cardinality lambda. We also prove two theorems that
characterize tightness of products of fans in terms of families of integer--
valued functions.
