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.
Categories: math.FA