Carathéodory Kernels and Farrell’s Theorem

Abstract

Given a sequence {G_n} of regions and a region G ≠ Ɉ such that G ⊆ G_n+1 ⊆ G_n for n = 1,2,3,.., we say that a superset G’ of G is suitable if G’ is connected and G’ ⊆ ∩G_n. Then ker[G_n: G], the kernel of {G_n} with respect to G, is defined as the union of all suitable supersets of G.