EN
In the paper a class of families 𝓕(M) of functions defined on differentiable manifolds M with the following properties:
$1_{𝓕}$. if M is a linear manifold, then 𝓕(M) contains convex functions,
$2_{𝓕}$. 𝓕(·) is invariant under diffeomorphisms,
$3_{𝓕}$. each f ∈ 𝓕(M) is differentiable on a dense $G_{δ}$-set,
is investigated.