Erratum and addendum to 'Recovering a compact Hausdorff space X from the compatibility ordering on C(X)' (Fund. Math. 242 (2018), 187-205)
2022
Abstrakt
It was kindly pointed out by L. G. Cordeiro as well as independently by
T. Bice and W. Kubis that the proof of Theorem 1.1 from the paper 'Recovering a compact
Hausdorff space X from the compatibility ordering on CpXq', Fund. Math. 242 (2018), 187-205 is flawed. We demonstrate that not only is the proof of the said statement erroneous but that there is indeed a counterexample to it; Theorems 1.2-1.3 remain unaffected though. 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.