Erratum to “Topological complexity is a fibrewise L–S category” [Topology Appl. 157 (1) (2010) 10–21]

There is a problem with the proof of Theorem 1.13 of Iwase and Sakai (2010) [2] which states that for a fibrewise well-pointed space X over B, we have and that for a locally finite simplicial complex B, we have TC(B)=TCM(B). While we still conjecture that Theorem 1.13 is true, this problem means that, at present, no proof is given to exist. Alternatively, we show the difference between two invariants and is at most 1 and the conjecture is true for some cases. We give further corrections mainly in the proof of Theorem 1.12.