Mathematica Eterna

Mathematica Eterna
Open Access

ISSN: 1314-3344


Generalizations of the Stone — Weierstrass theorem

Andriy Yurachkivsky

The classical Stone—Weierstrass theorem is generalized in two directions. In the first of them, the assumption of compactness of the domain of definition is weakened to countable compactness, and in the second, we waive topological assumptions at all, due to substitution of a topology by a convergence, and thereon the topological continuity by the sequential one.