Approximation of Continuously Differentiable Functions

This self-contained book brings together the important results of a rapidly growing area.As a starting point it presents the classic results of the theory. The book covers such results as: the extension of Wells'' theorem and Aron''s theorem for the fine topology of order m; extension of Bernstein''s and Weierstrass'' theorems for infinite dimensional Banach spaces; extension of Nachbin''s and Whitney''s theorem for infinite dimensional Banach spaces; automatic continuity of homomorphisms in algebras of continuously differentiable functions, etc.