Stone-Weierstrass theorems for group-valued functions (Q1885664)

Sternfeld introduced the concept of constructive group as a natural way to formulate Stone-Weierstrass type theorems. In this paper the authors address a question raised by \textit{Y. Sternfeld} [Constructive Approximation 6, No. 4, 339--351 (1990; Zbl 0709.41012)] as to which groups are constructive. It is proved that a locally compact group with more than 2 elements is constructive if it is either totally disconnected or homeomorphic to some vector group \((\mathbb{R})^n\).