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.
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The work of the first author was financially supported by the Ministry of Higher Education and Scientific Research of Iraq.
Communicated by Jörg Eschmeier.
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Al-shakarchi, S., Doust, I. \(AC(\sigma)\) spaces for polygonally inscribed curves. Banach J. Math. Anal. 15, 31 (2021). https://doi.org/10.1007/s43037-020-00110-w
- Functions of bounded variation
- Isomorphisms of function spaces
Mathematics Subject Classification