engleski

Using non-cofinite resolutions in shape theory. Application to Cartesian products

The strong shape category of topological spaces SSh can be defined using the coherent homotopy category CH and cofinite polyhedral resolutions of spaces. In the problem whether the Cartesian product $X\times P$ of a compact Hausdorf space <i>X</i> and a polyhedron <i>P</i> is a product in the category Sh, one encounters the difficulty that the natural polyhedral resolution, associated with <i>X × P</i>, is not a cofinite resolution. In the paper it is shown how one can overcome this difficulty.

strong shape ; Cartesian product ; cofinite polyhedral resolution

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