Commutative cochains of germs of differential forms for Euclidean compacta (Q602042)

The purpose of this paper is to construct for any compactum \(K \subset \mathbb R^n\) a space \(C^p(K)\) of commutative germs of \(C^{\infty }\)-differential \(p\)-forms, which is a reflexive locally convex topological vector space with \(C_p(K)\) as its dual. This work consists of the following basic parts: the space of cochain complexes for compact subsets of \(\mathbb R^n\), the space of chain complexes and (co-)homology groups, relative cohomology groups, and reflexive topological vector spaces of compacta in \(\mathbb R^n\).