A Banach space C

We show that if Jensen's diamond principle holds, then for every natural number n there is a compact space K, such that whenever L is compact space and the Banach spaces of continuous functions C(K) and C(L) are isomorphic, the covering dimension of L is equal to n. The constructed space K is a separable connected compact space with the property that every linear bounded operator T on C(K) is a weak multiplication i.e. it is of the form T=g*Id+S, where g is an element of C(K) and S is weakly compact.