Glasnik Matematicki, Vol. 33, No.2 (1998), 287-297.
PROPER n-SHAPE CATEGORIES
Institute of Mathematics, University of Tsukuba, Tsukuba 305-8571,
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
is the category whose objects are locally compact separable metrizable
spaces and whose morphisms are proper n-homotopy classes of
proper maps, and
is the full subcategory of
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.
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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