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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))
Proper $n$-Shape Categories
Katsuro Sakai,
Pages. 287-297
Abstract In this paper, it is shown that the proper $n$-shape category of Ball-Sher type
is isomorphic to a subcategory of the proper $n$-shape category defined by proper
$n$-shapings. It is known that the latter is isomorphic to the shape category
defined by the pair $(mathscr H_p ^n, mathscr H_p ^n text{Pol})$, where $mathscr H_p ^n$ is the category whose objects are locally compact separable metrizable spaces and whose morphisms are the proper $n$-homotopy classes of proper maps, and $mathscr H_p^n$ Pol is the Full subcategory of $mathscr H_p^n$ whose objects are spaces having the proper $n$-homotopy type of polyhedra. In case $n=infty$, this shows the relation between the original Ball-Sher's category and
the proper shape category defined by proper shapings. We also discuss the proper
$n$-shape category of spaces of dimension $leqslant n+1$.
Contents 1. Introduction
2. The proper $n$-shape theory
3. Proper $n$-fundamental nets and proper $n$-approximative maps
4. A categorical isomorphism between $mathscr S_p^n$ and $mathscr A_p^n$
5. Proper $n$-shapes of $(n+1)$-dimensional spaces
Key words Proper $n$-shape category, proper $n$-homotopy, proper $n$-fundamental net, proper $n$-approximative map, proper $n$-shaping, expansion
Mathmatical Subject Classification 54C56, 55P55