Let $U$ be an open semi-algebraic subset of $\mathbf{R}^n$ and let $X$ be a closed analytic subset of $U$ which is also a semi-algebraic set (e.g., $U = \mathbf{R}^n ...

Various classes of analytic, quasi-analytic and other infinitely differentiable functions of a real variable are studied. The paper gives a self-contained treatment by means of an elementary real ...