engleski

Strictly canonical PL resolutions of spaces and mappings

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 beddings. This demonstrates that arbitrary spaces and mappings can be expressed in terms of simple spaces (polyhedra) and simple mappings (strictly canonical, piecewise linear and simplicial). Therefore, our result is an improvement to the well known theorem due to S.,Mardešić, which provides existence of polyhedral resolutions of spaces and mappings, with no final specification on projections, bonding mappings or mappings between the terms of the systems. Furthermore, an application on certain classes of paracompact spaces and their mappings yields important characterizations.

simplicial complex; polyhedron; simplicial mapping; PL mapping; normalcovering; nerve; (strictly) canonical mapping; inverse system;resolution; paracompact space

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