  We construct two universes V_1, V_2 satisfying the following: GCH below
\aleph_\omega, 2^{\aleph_\omega} = \aleph_{\omega+2} and the topological
density of the space 2^{\aleph_\omega} with \aleph_0 box product topology is
\aleph_{\omega+1} in V_1 and \aleph_{\omega+2} in V_2. Further related results
are discussed as well.

Logic