… In particular we state the existence of differentiable global bases for a differentiable family
of subspaces, having … In fact we prove in (IV-l-2) two local characterizations of such families: …

… Let (u0,...,un) ⊂ C∞ (K) be a finite family and let F be an infinite dimensional subspace of
C∞ (K). For every real number ε > 0, there exists un+1 ∈ F with un+1 ∞ = 1 and such that …

… 4 compares our definition of differentiable space with those of JW Smith and KT Chen, …
differentiable space, andY a topological subspace of X. One makes Y a differentiable subspace …

… differentiable subspaces and may define the fibre of any morphism of differentiable spaces
over a subspace … smooth manifold V is a family of global differentiable functions {i}ie such that …

… generated by a family of weights Vk. For the space CVk(Ω,E) and its subspace CVk 0 (Ω,E) of
… We define the topological subspace of CVk(Ω,E) consisting of the functions that vanish with …

… be dealing with families of closed separable subspaces of a … taking into account that f is
Fréchet differentiable at x if (and only if) … of a rich family of separable subspaces that guarantees …

… We present fundamental notions of points and subspaces of projective Klingenberg spaces.
… In the family of submodules U(M) we mark proper subsets of all A-subspaces of the module …

… subspaces 6. An application of fixed point principles for holomorphic operators to the invariant
semi-definite subspace … of arbitrary families of factors. However, in the case of countable …

… subspaces of R(E) (C(E)). Finally, if E is a domain in n-dimensional Euclidean space, then
the set (E) of all I times differentiable … For instance, a family of differentiable functions on a …

… of Laurent Schwartz concerning division of distributions and differentiable functions, and on
the other by the theory of singularities of differentiable mappings, developed at first by Thom …