In recent papers S. Mardešič
and J. Segal have used ANR-systems to obtain an alternate approach to
Borsuk’s shape theory. At the same time, they have extended the theory
to include all compact Hausdorff spaces. In this paper some of the results
of Mardesič and Segal are used to obtain Borsuk’s fundamental groups,
and to extend some of Borsuk’s results that relate shapes and products to
arbitrary products. A result relating (direct) products and shape groups is also
obtained.