Shape groups and products

Abstract

In recent papers S. Mardesic 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 Mardesic 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.