engleski

The standard resolution of the product of a compactum and a polyhedron consists of ANEs for metric spaces

In order to study (strong) shape properties of the Cartesian product X x P of a compact Hausdorff space X and a (non- compact) polyhedron P, the author has introduced in 2003 a resolution q: X x P --> Y, where Y=(Y_a, q_{; ; ; ; aa'}; ; ; ; , M) is an inverse system consisting of paracompact spaces Y_a, having the homotopy type of polyhedra. In the present paper, it is proved that the spaces Y_a are stratifiable k-spaces, which are absolute neighborhood extensors for metric spaces. This makes it possible to use the homotopy extension property, for pairs of metric spaces (X, A), A closed in X, and maps F: (A x I) U (X x 0) - -> Y_a, a result needed in various arguments concerning the shape of products X x P.

Inverse system ; inverse limit ; resolution ; direct limit ; Cartesian product ; absolute neighborhood extensor (ANE) ; stratifiable space ; shape.

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