TY - JOUR

T1 - Erratum to "Topological complexity is a fibrewise L-S category" [Topology Appl. 157 (1) (2010) 10-21]

AU - Iwase, Norio

AU - Sakai, Michihiro

N1 - Funding Information:
* Corresponding author. E-mail addresses: iwase@math.kyushu-u.ac.jp (N. Iwase), sakai@kurume-nct.ac.jp (M. Sakai). 1 Supported by the Grant-in-Aid for Scientific Research #22340014 from Japan Society for the Promotion of Science.

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 well-pointed 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 well-pointed 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.

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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 - 0166-8641

IS - 10-11

ER -