Whitney’s Extension Theorem in O-minimal Context

Model theory seminarFriday, March 20, 201512:30 pmGC 6417

Whitney’s Extension Theorem in O-minimal Context

Ohio State University

Let $U$ be an open subset of $R^n$ and $f$, a function from $U$ to $R$, be $C^m$. We call the collection of $f$ and its derivatives, the jet of order $m$ of $f$. In 1934, H. Whitney asked how can we determine whether a collection of continuous functions on a closed subset of $R^n$ is a jet of order $m$ of a $C^m$-function and also gave a solution to this question which is known as Whitney’s Extension Theorem.
In this talk, let $R$ be an o-minimal expansion of the real field. We discuss whether a collection of continuous functions on a closed subset of $R^n$ is a jet of order $m$ of a $C^m$-function which is definable in $R$.

Posted by on February 20th, 2015