Vol. 48, No. 2, 1973

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Shape groups and products

Thomas Jay Sanders

Vol. 48 (1973), No. 2, 485–496

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.

Mathematical Subject Classification 2000
Primary: 54C56
Secondary: 55E99
Received: 23 June 1972
Revised: 3 August 1972
Published: 1 October 1973
Thomas Jay Sanders