Abstract
There is a problem with the proof of Theorem 1.13 of Iwase and Sakai (2010) [2] which states that for a fibrewise wellpointed space X over B, we have cat _{B}B(X)=cat _{B} ^{*}(X) and that for a locally finite simplicial complex B, we have TC(B)=TC ^{M}(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 cat _{B} ^{*}(X) and cat _{B} ^{B}(X) is at most 1 and the conjecture is true for some cases. We give further corrections mainly in the proof of Theorem 1.12.
Original language  English 

Pages (fromto)  28102813 
Number of pages  4 
Journal  Topology and its Applications 
Volume  159 
Issue number  1011 
DOIs 

Publication status  Published  Jun 15 2012 
All Science Journal Classification (ASJC) codes
 Geometry and Topology
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Iwase, N., & Sakai, M. (2012). Erratum to "Topological complexity is a fibrewise LS category" [Topology Appl. 157 (1) (2010) 1021]. Topology and its Applications, 159(1011), 28102813. https://doi.org/10.1016/j.topol.2012.03.009