Duality in manifolds

Summary For the purpose of presenting general Alexander-duality-theorems (§7), strong-shape-homology _* and cohomology _* with coefficients in an arbitrary spectrum E turns out to be the appropriate implement. Therefore the main properties of _* and _* are (analogously to those of ordinary (co-) homology with coefficients in E) developed (§§3-5). In order to be able to perform the necessary constructions, strong-shape-theory and in particular two different kinds of smash-products in this shape-category are treated (§§1,2, appendix). All previously known Alexander-duality theorems appear as special cases of the main theorems of this paper (§8).