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

### THE EXISTENCE OF *n*-SHAPE THEORY FOR
ARBITRARY COMPACTA

### Rolando Jimenez and Leonard R. Rubin

Instituto de Matematicas, Unidad Morelia, Nicolas Romero 150, Centro
Morelia, Mexico

*e-mail:* `rolando@gauss.matem.unam.mx`
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.

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