$AC(\sigma )$ 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.

17 pages. Minor corrections to version 1

References in corpus (1)

• Isomorphisms of $AC(\sigma )$ spaces for countable sets

Cited by in corpus (1)

• The Banach algebras $AC(\sigma )$ and $BV(\sigma )$