  The paper is concerned with defining a topology on the set of ideals of
codimension d of the algebra C^\infty(M,R) with M being a compact smooth
manifold. Its main property is that it is compact Hausdorff and it contains as
a subspace the configuration space of d distinct unordered points in M and
therefore provides a "compactification" of this configuration space. It
naturally forms a space over the symmetric product SP_d(M) and as such has a
very rich structure. Moreover it is covered by a (naturally defined) set of
charts in which it is semialgebraic.
