论文标题
部分可观测时空混沌系统的无模型预测
Borsuk-Ulam property and Sectional Category
论文作者
论文摘要
对于Hausdorff Space $ X $，免费互动$τ：X \ to X $和Hausdorff Space $ Y $，我们发现了双重覆盖$ Q的部分类别$ Q：x/τ$ x/τ$和$ q^y：f（y，2） $ d（y，2）= f（y，2）/σ_2$，以及三重$ \ left（（x，x，τ）; y \ right）$的borsuk-ulam属性（bup）。明确地，我们证明了三重$ \ left（（x，τ）; y \ right）$如果$ q $的截面类别大于$ q^y $的截面类别。该属性将Borsuk-Ulam理论中的标准问题与部分类别的当前研究趋势联系起来。作为结果的应用，我们表明$（x，τ）$的索引与商映射的截面类别$ q：x \ x/τ$减1 $ q：x/τ$减1 $ x $。此外，我们还提出了有关Borsuk-Ulam理论和部分类别的一些新结果。
For a Hausdorff space $X$, a free involution $τ:X\to X$ and a Hausdorff space $Y$, we discover a connection between the sectional category of the double covers $q:X\to X/τ$ and $q^Y:F(Y,2)\to D(Y,2)$ from the ordered configuration space $F(Y,2)$ to its unordered quotient $D(Y,2)=F(Y,2)/Σ_2$, and the Borsuk-Ulam property (BUP) for the triple $\left((X,τ);Y\right)$. Explicitly, we demonstrate that the triple $\left((X,τ);Y\right)$ satisfies the BUP if the sectional category of $q$ is bigger than the sectional category of $q^Y$. This property connects a standard problem in Borsuk-Ulam theory to current research trends in sectional category. As an application of our results, we show that the index of $(X,τ)$ coincides with the sectional category of the quotient map $q:X\to X/τ$ minus 1 for any paracompact space $X$. In addition, we present some new results relating Borsuk-Ulam theory and sectional category.
