Erratum and addendum to `Recovering a compact Hausdorff space $X$ from the compatibility ordering on $C(X)$'
Volume 257 / 2022
Fundamenta Mathematicae 257 (2022), 217-228
MSC: Primary 46E10, 46T20; Secondary 06F25.
DOI: 10.4064/fm170-2-2022
Published online: 24 February 2022
Abstract
It was kindly pointed out by L. G. Cordeiro as well as independently by T. Bice and W. Kubiś that the proof of Theorem 1.1 from the paper in the title is flawed. We salvage the result in the class of totally disconnected compact spaces and we propose an amendment by a suitable modification of the compatibility ordering that yields the conclusion of Theorem 1.1 for arbitrary compact spaces. Moreover, we demonstrate that there is a compatibility isomorphism between the spaces of continuous functions on the unit disc and a closed annulus.
