AC(σ) spaces for polygonally inscribed curves

Abstract

For certain families of compact subsets of the plane, the isomorphism class of the algebra of absolutely continuous functions on a set is completely determined by the homeomorphism class of the set. This is analogous to the Gelfand--Kolmogorov theorem for C(K) spaces. In this paper we define a family of compact sets comprising finite unions of convex curves and show that this family has the `Gelfand--Kolmogorov' property.