  Let $X$ be a compact metric space, $C(X)$ be the space of continuous
real-valued functions on $X$, and $A_1$, $A_2$ be two closed subalgebras of
$C(X)$ containing constant functions. We consider the problem of approximation
of a function $f\in C(X)$ by elements from $A_1+A_2$. We prove a Chebyshev type
alternation theorem for a function $u_0\in A_1+A_2$ to be a best approximation
to $f$.

Functional Analysis