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 
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All Science Journal Classification (ASJC) codes
 Geometry and Topology
Cite this
Erratum to "Topological complexity is a fibrewise LS category" [Topology Appl. 157 (1) (2010) 1021]. / Iwase, Norio; Sakai, Michihiro.
In: Topology and its Applications, Vol. 159, No. 1011, 15.06.2012, p. 28102813.Research output: Contribution to journal › Comment/debate
}
TY  JOUR
T1  Erratum to "Topological complexity is a fibrewise LS category" [Topology Appl. 157 (1) (2010) 1021]
AU  Iwase, Norio
AU  Sakai, Michihiro
PY  2012/6/15
Y1  2012/6/15
N2  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 BB(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.
AB  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 BB(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.
UR  http://www.scopus.com/inward/record.url?scp=84861329522&partnerID=8YFLogxK
UR  http://www.scopus.com/inward/citedby.url?scp=84861329522&partnerID=8YFLogxK
U2  10.1016/j.topol.2012.03.009
DO  10.1016/j.topol.2012.03.009
M3  Comment/debate
AN  SCOPUS:84861329522
VL  159
SP  2810
EP  2813
JO  Topology and its Applications
JF  Topology and its Applications
SN  01668641
IS  1011
ER 