Abstract: In what follows, C will be a compact Hausdorff space, and 
will be a uniformly closed separating algebra of continuous complexvalued functions on C. That is, sums, products, and complex multiples of elements of 
are in 
, uniform limits of elements of 
are in 
, and for distinct points x and y in C there exists f in 
with f(x)≠f(y). Šilov (see [1]) has shown that there exists a smallest closed subset B of C, called the Šilov boundary of 
such that for each f in 
there exists x in B with |f(x)| = ∥f∥, where ∥f∥ = max {|f(y)| : y∈C}. The following theorem generalizes this result, in case C is metric…
