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We introduce an exchange natural isomorphism between iterated higher order jet functors depending on a classical linear connection on the base manifold. As an application we study the prolongation of higher order connections to jet bundles.
In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties:
. if M is a linear manifold, then (M) contains convex functions,
. (·) is invariant under diffeomorphisms,
. each f ∈ (M) is differentiable on a dense -set,
is investigated.
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