Abstract
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 ${\rm secat}_k(f)={\rm secat}(\mathcal{B}(f))$ for sufficiently large $k$, where $\mathcal{B}(f)$ is the induced map on the associated polyhedra.
Citation
Kohei Tanaka. "Sectional category of maps related to finite spaces." Topol. Methods Nonlinear Anal. 63 (2) 537 - 557, 2024. https://doi.org/10.12775/TMNA.2023.029
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