On the Stone-Weierstrass theorem for group-valued functions.
by
Jorge Galindo
Dpto. de Matematicas, Universitat Jaume I , Castellon (Spain)
Coauthors: Manuel Sanchis

In this talk we shall be looking for Stone-Weierstrass-type theorems for groups of continuous group-valued functions. Our approach to the problem will be marked by the concept of constructive group introduced by Sternfeld (Dense subgroups of C(K)-Stone-Weierstrass-type theorems for groups, Constr. Approx. 6 (1990) ) that is based on the fact that a vector subspace of C(X, R) stable under composition with certain maps (like x --> x²) is automatically a subalgebra. A characterization of locally compact constructive groups will be presented and, as a particular case, we shall show that a locally compact connected group is constructive (and thus satisfy a suitable version of the Stone-Weierstrass theorem) if and only if it contains no compact subgroup or, what is equivalent by virtue of Iwasawa's theorem, if and only if it decomposes as the product of a finite family of subgroups topologically isomorphic to R.

Date received: May 2, 2003