Glasnik Matematicki, Vol. 33, No.2 (1998), 299-321.

DESCRIBING THE PROPER n-SHAPE CATEGORY BY USING NON-CONTINUOUS FUNCTIONS

Yuji Akaike and Katsuro Sakai

Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan
e-mail: sakaiktr@sakura.cc.tsukuba.ac.jp

Abstract.   In this paper, we describe the proper n-shape category by using non-continuous functions. Moreover, applying non-continuous homotopies, we show that the Cech expansion is a polyhedral expansion in the proper n-homotopy category.

1991 Mathematics Subject Classification.   54C56, 55P55.

Key words and phrases.   U-continuous, properly (U,n)-homotopic, proper n-shape.