  In his previous works the author introduced the notion of the stereotype
approximation property as an analog of the classical approximation property
transferred to the category ${\tt Ste}$ of stereotype spaces. It is known, that
the study of this property is much more difficult than in the classical theory,
since the spaces of operators in the category ${\tt Ste}$ are defined in a more
complicated way. In this note, it is proved that the algebra $C(M)$ of
continuous functions on an arbitrary complete (not necessarily locally compact)
metric space $M$ has the stereotype approximation property.
