Glasnik Matematicki, Vol. 32, No.1 (1997), 125-140.


B. Cervar and N. Uglesic

Department of Mathematics, University of Split, Teslina 12/III, 21000 Split, Croatia

Abstract.   A strictly canonical PL resolution of a space, as well as of a mapping, is constructed. Moreover, in the case of a mapping, the mappings between terms of the two systems are simplicial embeddings. This demonstrates that arbitrary spaces and mappings can be expressed in terms of simple spaces (polyhedra) and simple mappings (strictly canonical, picewise linear and simplicial). Therefore, our result is an improvement of the well known theorem due to S. Mardesic, which provides existence of polyhedral resolutions of spaces and mappings, with no final specification on projections, bonding mappings or mappings between the terms of systems. Furthermore, an application on certain classes of paracompact spaces and their mappings yields important characterizations.

1991 Mathematics Subject Classification.   54B52, 54C10, 57Q05.

Key words and phrases.   Simplicial complex, polyhedron, simplicial mapping, PL mapping, normal covering, nerve, (strictly) canonical mapping, inverse system, resolution, paracompact space.

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