The closed model category of exterior spaces, that contains the proper category, is a useful tool for the study of non compact spaces and manifolds. The notion of exterior weak N-Sequivalences is given by exterior maps which induce isomorphisms on the k-th N-exterior homotopy groups πN k for k ∈ S, where S is a set of non negative integers. The category of exterior spaces with a base ray locali...

A Stein covering of a complex manifold may be used to realise its analytic cohomology in accordance with the Čech theory. If, however, the Stein covering is parameterised by a smooth manifold rather than just a discrete set, then we construct a cohomology theory in which an exterior derivative replaces the usual combinatorial Čech differential. Our construction is motivated by integral geometry...