Analogue of Whitney's extension theorem - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T06:50:55Z http://mathoverflow.net/feeds/question/52722 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/52722/analogue-of-whitneys-extension-theorem Analogue of Whitney's extension theorem Hugo Chapdelaine 2011-01-21T04:26:51Z 2011-01-21T04:26:51Z <p>So let $n,m$ be two strictly positive numbers. Let $A\subseteq\mathbf{R}^n$ be a compact $C^{\infty}$-submanifold (possibly with boundary and of real dimension not necessarily equal to $n$). Let $f:A\rightarrow \mathbf{R}^m$ be a smooth function. Then is it always possible to extend $f$ in a smooth way to all of $\mathbf{R}^n$?</p> <p>Is there a good textbooks where such extension results are discussed extensively? </p>