Correction

30 Apr. 2026
This document is to correct an error in the following paper:

39. Magnitude homology of metric spaces and order complexes. Bull. of London Math. Soc. vol. 53 (2021) 893-905. arXiv:1803.04247. (March 1 2018)

Theorem 4.4 of the above paper does not hold if the space contains 4-cuts. The correct assertion is "if the length of the frame $|F|$ is less than the infimum of the lengths of 4-cuts $m_X$, then there is an isomorphism of chain complexes ...". (A weaker assumption "the length of consecutive three points $(a_{i-1}, a_i, a_{i+1})$ in $F$ is less than $m_X$" would be enough.)

Acknowledgment: I appreciate Ye Liu and Junnosuke Koizumi for pointing out this.