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arXiv · 1312.2304

Isomorphisms of $AC(σ)$ spaces

Ian Doust·Michael Leinert
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Abstract

Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if $AC(σ_1)$ is algebra isomorphic to $AC(σ_2)$ then $σ_1$ is homeomorphic to $σ_2$. The converse however is false. In a positive direction we show that the converse implication does hold if the sets $σ_1$ and $σ_2$ are confined to a restricted collection of compact sets, such as the set of all simple polygons.

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Ian Doust, Michael Leinert. 2013-12-09. Isomorphisms of $AC(σ)$ spaces. https://arxiv.org/abs/1312.2304

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