Glasnik Matematicki, Vol. 33, No.1 (1998), 123-132.

THE EXISTENCE OF n-SHAPE THEORY FOR ARBITRARY COMPACTA

Rolando Jimenez and Leonard R. Rubin

Department of Mathematics, The Univesity of Oklahoma, 601 Elm Avenue, Room 423, Norman, OK 73019, USA
e-mail: lrubin@ou.edu

Abstract.   Shape theory is an extension of homotopy theory which uses the idea of homotopy in its conception. By comparision, the theory of n-shape, which heretofore only has been defined for metrizable compacta, has as its basic notion that of n-homotopy instead of homotopy. We shall demonstrate that the theory of n-shape extends to the class of all Hausdorff compacta.

1991 Mathematics Subject Classification.   55P55.

Key words and phrases.   Dimension, shape theory, n-shape theory, approximate inverse system.