Applications of Nachbin’s Theorem concerning Dense Subalgebras of Differentiable Functions

ABSTRACT

In this paper, we give some applications of Nachbin’s Theorem ⁽⁴⁾ to approximation and interpolation in the the space of all k times continuously differentiable real functions on any open subset of the Euclidean space.

Keywords:
Nachbin’s theorem; approximation of differentiable functions; Stone-Weierstrass theorem; interpolation