A characterization of maps in which can be approximated by smooth maps
A correction to a paper of H. King.
A fixed point theorem for a class of multi-valued continuously differentiable maps
A generalized sharp Whitney theorem for jets.
Suppose that, for each point x in a given subset E ⊂ Rn, we are given an m-jet f(x) and a convex, symmetric set σ(x) of m-jets at x. We ask whether there exist a function F ∈ Cm,w(Rn) and a finite constant M, such that the m-jet of F at x belongs to f(x) + Mσ(x) for all x ∈ E. We give a necessary and sufficient condition for the existence of such F, M, provided each σ(x) satisfies a condition that we call "Whitnet w-convexity".
A generic condition implying o-minimality for restricted C-functions
We prove that the expansion of the real field by a restricted C-function is generically o-minimal. Such a result was announced by A. Grigoriev, and proved in a different way. Here, we deduce quasi-analyticity from a transcendence condition on Taylor expansions. This then implies o-minimality. The transcendance condition is shown to be generic. As a corollary, we recover in a simple way that there exist o-minimal structures that doesn’t admit analytic cell decomposition, and that there exist incompatible...
A metric tangential calculus.
A Note on Right-Equivalence of Map-Germs.
A Note on the Order of Determination of a Finitely Determined Germ.
A regularity lemma for functions of several variables.
We shall prove the following Theorem. Let Fs and Fu be two continuous transverse foliations with uniformly smooth leaves, of some manifold. If f is uniformly smooth along the leaves of Fs and Fu, then f is smooth.
A semi-global Taylor formula for manifolds
A splitting lemma for non-reflexive Banach spaces.
A Splitting Theorem for Maps Into IR2 .
A Sufflcient Condition for a Critical Point of a Functional to be a Minimum and Its Application to Plateau' s Problem.
A theorem on the escape from the space of hyperbolic polynomials.
Algebras Q (f) Determine the Topological Types of Generic Map-Germs.
An algebraic construction of the generic singularities of Boardman-Thom
An analog of Sard's theorem for -smooth functions of two variables.
An arithmetic characterisation of the symmetric monodromy groups of singularities.
An Example of Moduli for Singular Symplec-tic Forms
An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence