Glasnik Matematicki, Vol. 33, No.2 (1998), 287-297.


Katsuro Sakai

Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571, Japan

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-shaping. It is known that the latter is isomorphic to the shape category defined by the pair (Hpn, Hpn Pol), where Hpn is the category whose objects are locally compact separable metrizable spaces and whose morphisms are proper n-homotopy classes of proper maps, and Hpn Pol is the full subcategory of Hpn whose objects are spaces having the proper n-homotopy type of polyhedra. In the case n = ∞, 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 space of dimension n + 1.

1991 Mathematics Subject Classification.   54C56, 55P55.

Key words and phrases.   Proper n-shape category, proper n-homotopy, proper n-fundamental net, proper n-approximative net, proper n-shaping, expansion.

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