1School of Mathematics and Statistics University of New South Wales Sydney 2052 Australia 2Institut für Angewandte Mathematik Universität Heidelberg Im Neuenheimer Feld 294 D-69120 Heidelberg, Germany
Studia Mathematica, Tome 228 (2015) no. 1, pp. 7-31
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 $AC(\sigma _1)$ is algebra isomorphic to $AC(\sigma _2)$ then $\sigma _1$ is homeomorphic to $\sigma _2$. The converse however is false. In a positive direction we show that the converse implication does hold if the sets $\sigma _1$ and $\sigma _2$ are confined to a restricted collection of compact sets, such as the set of all simple polygons.
1
School of Mathematics and Statistics University of New South Wales Sydney 2052 Australia
2
Institut für Angewandte Mathematik Universität Heidelberg Im Neuenheimer Feld 294 D-69120 Heidelberg, Germany
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Ian Doust; Michael Leinert. Isomorphisms of $AC(\sigma )$ spaces. Studia Mathematica, Tome 228 (2015) no. 1, pp. 7-31. doi: 10.4064/sm228-1-3
