Smooth approximation theorem for differential manifolds
This fact is an application of the following pivotal fact/result/idea: Stone-Weierstrass theorem
View other applications of Stone-Weierstrass theorem OR Read a survey article on applying Stone-Weierstrass theorem
This article gives a result on smooth approximation; a result stating that a continuous map can be replaced by a smooth map satisfying similar properties
Let and be differential manifolds and define to be the space of all continuous maps from to , endowed with the compact-open topology. Let be the space of all smooth maps from to , viewed as a subset of . Then is dense in .