Erratum to "Topological complexity is a fibrewise L-S category''
Erratum to "Topological complexity is a fibrewise L-S category''
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“拓扑复杂性是纤维 L-S 类别”的勘误
DOI：
10.1016/j.topol.2012.03.009
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Michihiro
中科院分区：
文献类型：
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作者：
Iwase;Norio; Sakai;Michihiro
关于Iwase和Sakai(2010)[2]的定理1.13的证明存在一个问题，该证明表明，对于B上的纤维井尖空间X，我们有catBB(X)=catB (X)，对于局部有限简单复空间B，我们有TC(B)=TCM(B)。虽然我们仍然推测定理1.13是正确的，但这个问题意味着，目前还没有证据证明它的存在。或者，我们证明了两个不变量catB (X)和catBB(X)之间的差不超过1，并且猜想在某些情况下是正确的。我们主要在定理1.12的证明中作进一步的修正。
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 catBB(X)=catB⁎(X) 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 catB⁎(X) and catBB(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.