Isomorphisms between spaces of vector-valued continuous functions

A theorem due to Milutin [ 12 ] (see also [ 13 ]) asserts that for any two uncountable compact metric spaces Ω 1 and Ω 2 the spaces of continuous real-valued functions C (Ω 1 ) and C (Ω 2 ) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then C (Ω 1 ; X ) and C (Ω 2 ; X ) are isomorphic.