Take the tour ×  Does anyone know where I can find a reference
for the following well-known fact:  Let $(X_i)_{i\in I}$ be a
family of compact Hausdorff spaces and let $X$ be the disjoint
sum of all $X_i$s.   $c_0(I, C(X_i)) = C_0(X)$,  where the left
hand side stands for the $c_0$-sum (possibly uncountable) of
$C(X_i)$s.  share|improve this question It might be difficult to
locate this formally proven in the literature. I only saw this
stated as an exercise or as an obvious (or well-known) fact. For
example, Conway's Course in Functional Analysis, chapter VII.1,
exercise 9. –  Martin Jan 30 at 21:44 I could provide a proof,
if you want, but you seem to be more interested in a reference.
–  Martin Jan 30 at 21:49 Thanks! The proof is rather easy. I
think this is enough for me, you can post is as an answer. – 
user60253 Jan 30 at 22:04 add comment  1 Answer  up vote 2 down
vote accepted  Since the result is quite easy to prove, it is
mostly stated as an exercise or as an obvious fact.  For
example, Conway, A C