Isomorphisms of BV(?) spaces

In this paper we investigate the relationship between properties of a compact set $\sigma \subseteq \mathbb{C}$ and structure space $BV(\sigma)$ functions bounded variation (in sense Ashton Doust) defined on $\sigma$. For subalgebras absolutely continuous $\sigma$, it is known that for certain classes sets one obtains Gelfand--Kolmogorov type result: function spaces $AC(\sigma_1)$ $AC(\sigma_2)$ are isomorphic if only domain $\sigma_1$ $\sigma_2$ homeomorphic. Our main theorem in case isomorphism must extend to an spaces. An application given spectral theory $AC(\sigma)$ operators.