APPROXIMATE RESOLUTIONS IN STRONG SHAPE THEORY by Bernd Günther, Frankfurt, Germany

Abstract. By adding a coherent system of homotopies to an approximate inverse system of ANR-spaces of polyhedra in the sense of Mardešıć, Rubin and Watanabe we integrate the theory of approximate systems into coherent homotopy theory. When applied to an approximate resolution of a space this process leads to a strong expansion and hence determines the strong shape of that space. Mathematics subject classification: 54C56, 55P99, 55U99. Keywords: Approximate inverse systems, resolutions, shape, coherent sytems, strong expansions.