• The standard resolution of the product of a compactum and a polyhedron consists of ANEs for metric spaces, Vol 36, No.3

Mardešić, Sibe, University of Zagreb, Zagreb, Croatia (smardes@math.hr)
The standard resolution of the product of a compactum and a polyhedron consists of ANEs for metric spaces, pp. 887-904.
ABSTRACT. In order to study (strong) shape properties of the Cartesian product of a compactum X and a (non-compact) polyhedron P, the author has introduced in 2003 a particular resolution of such a product. It is an inverse limit of the product to an inverse system Y having some additional properties. The system Y consists of paracompact spaces Yμ, μ in M, having the homotopy type of polyhedra. In the present paper, it is proved that the spaces Yμ are stratifiable k-spaces and absolute neighborhood extensors for metric spaces. This makes it possible to use the homotopy extension property, for pairs of metric spaces, a result needed in various arguments concerning the shape of Cartesian products of a compactum X and a polyhedron P.

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The standard resolution of the product of a compactum and a polyhedron consists of ANEs for metric spaces, Vol 36, No.3

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