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

Norio Iwase, Michihiro Sakai

研究成果: ジャーナルへの寄稿コメント/討論

6 引用 (Scopus)

抄録

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.

元の言語英語
ページ(範囲)2810-2813
ページ数4
ジャーナルTopology and its Applications
159
発行部数10-11
DOI
出版物ステータス出版済み - 6 15 2012

Fingerprint

Topological Complexity
Topology
Theorem
Simplicial Complex
Invariant

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

これを引用

Erratum to "Topological complexity is a fibrewise L-S category" [Topology Appl. 157 (1) (2010) 10-21]. / Iwase, Norio; Sakai, Michihiro.

:: Topology and its Applications, 巻 159, 番号 10-11, 15.06.2012, p. 2810-2813.

研究成果: ジャーナルへの寄稿コメント/討論

@article{7a7d1e0be3834b07aee6e35edf797f29,
title = "Erratum to {"}Topological complexity is a fibrewise L-S category{"} [Topology Appl. 157 (1) (2010) 10-21]",
abstract = "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.",
author = "Norio Iwase and Michihiro Sakai",
year = "2012",
month = "6",
day = "15",
doi = "10.1016/j.topol.2012.03.009",
language = "English",
volume = "159",
pages = "2810--2813",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "10-11",

}

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

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.

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

VL - 159

SP - 2810

EP - 2813

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 10-11

ER -