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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 33 NO.2 / (1998))
Describing the Proper $n$-Shape Category by Using Non-Continuous Functions
Yuji Akaike, Katsuro Sakai,
Pages. 299-321
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.
Contents 1. Introduction
2. Preliminaries
3. Proper $mathscr V$-continuous functions
4. Proper proximate nets
5. The proper $n$-shape theory and the Cech expansion
6. A categorical isomorphism
7. Approach by using multi-valued maps
8. Remarks on the $n$-shape theory
Key words $mathscr U$-continuous, property $(mathscr U, n)$ -homotopic, proper $n$-shape
Mathmatical Subject Classification 54C56, 55P55