4 papers · 1 filter
Inner Lipschitz approximation in o-minimal structures
Nhan Nguyen, Anna Valette, Guillaume Valette
Given an o-minimal structure, we show that every definable (in this structure) mapping that is Lipschitz with respect to the inner metric can be approximated by map…
A remark on definable equivalence
Anna Valette, Guillaume Valette
We establish that if a submanifold of is definable in some o-minimal structure then any definable submanifold which is $\mathscr{C}^\inft…
Efroymson's approximation theorem for globally subanalytic functions
Anna Valette, Guillaume Valette
Efroymson's approximation theorem asserts that if is a semialgebraic mapping on a semialgebraic submanifold of and if $\…
A generalized Sard theorem on real closed fields
Anna Valette, Guillaume Valette
We work with semi-algebraic functions on arbitrary real closed fields. We generalize the notion of critical values and prove a Sard type theorem in our framework.