Diffeomorphism Group of the Real Line, Endowed with the Whitney Topology

In this paper we recognize the topological type of the group D(R) of C diffeomorphisms of the real line, endowed with the Whitney C-topology (cf. [6]). Besides the whole group D(R) we shall also be interested in its subgroup D c (R) ⊂ D (R) consisting of diffeomorphisms f : R → R with compact support supp(f) = clR{x ∈ R : f(x) 6= x}. For n = 0 the topological group D(R) turns into the homeomorphism group H(R) of R endowed with the Whitney topology and D c (R) turns into the subgroup Hc(R) of H(R) consisting of homeomorphisms with compact support. According to [1], the topological group Hc(R) is homeomorphic to the subgroup