In this paper, we will apply the Stone-Weierstrass Theorem to study some properties of the spaces of continuous functions on compact spaces. As a consequence, we will be able to construct a decreasing sequence of linear span dense subspaces in $C[0,1]$.
"Some Applications of the Stone-Weierstrass Theorem." Missouri J. Math. Sci. 3 (2) 79 - 83, Spring 1991. https://doi.org/10.35834/1991/0302079