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arXiv · 2007.05702

$AC(\sigma)$ spaces for polygonally inscribed curves

Shaymaa Al-shakarchi·Ian Doust
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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.

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BibTeXRIS

Shaymaa Al-shakarchi, Ian Doust. 2020-07-11. $AC(\sigma)$ spaces for polygonally inscribed curves. https://doi.org/10.1007/s43037-020-00110-w

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