与有限空间有关的映射的部分类别

Pub Date : 2024-03-03 DOI:10.12775/tmna.2023.029

Kohei Tanaka

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引用次数: 0

摘要

在本研究中，我们计算了一些与有限空间相关的连续映射 $f$ 的截面类别 secat$(f)$ 和截面数 sec$(f)。此外，我们利用 $k$th barycentric 细分为有限空间之间的映射 $f$ 引入了一个不变量 secat$_k(f)$，并证明了在足够大的 $k$ 条件下，secat$_k(f)=$ secat$(\mathcal{B}(f))$，其中 $\mathcal{B}(f)$ 是相关多面体上的诱导映射。

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Sectional category of maps related to finite spaces

In this study, we compute some examples of sectional category secat$(f)$ and sectional number sec$(f) for continuous maps $f$ related to finite spaces. Moreover, we introduce an invariant secat$_k(f)$ for a map $f$ between finite spaces using the $k$-th barycentric subdivision and show the equality secat$_k(f)=$ secat$(\mathcal{B}(f))$ for sufficiently large $k$, where $\mathcal{B}(f)$ is the induced map on the associated polyhedra.

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