{"title":"Sectional category of maps related to finite spaces","authors":"Kohei Tanaka","doi":"10.12775/tmna.2023.029","DOIUrl":null,"url":null,"abstract":"In this study, we compute some examples of sectional category secat$(f)$\nand sectional number sec$(f) for continuous maps $f$ related to finite spaces.\nMoreover, we introduce an invariant secat$_k(f)$ for a map $f$ between finite\n spaces using the $k$-th barycentric subdivision and show the equality\nsecat$_k(f)=$ secat$(\\mathcal{B}(f))$ for sufficiently large $k$, where $\\mathcal{B}(f)$\nis the induced map on the associated polyhedra.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Methods in Nonlinear Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12775/tmna.2023.029","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
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
secat$_k(f)=$ secat$(\mathcal{B}(f))$ for sufficiently large $k$, where $\mathcal{B}(f)$
is the induced map on the associated polyhedra.
期刊介绍:
Topological Methods in Nonlinear Analysis (TMNA) publishes research and survey papers on a wide range of nonlinear analysis, giving preference to those that employ topological methods. Papers in topology that are of interest in the treatment of nonlinear problems may also be included.