{"title":"强尺寸等级的不可还原性","authors":"Alejandro Illanes, Verónica Martínez-de-la-Vega","doi":"10.1515/ms-2024-0039","DOIUrl":null,"url":null,"abstract":"Given a continuum <jats:italic>X</jats:italic>, <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) denotes the hyperspace of nonempty closed subsets of <jats:italic>X</jats:italic> with at most <jats:italic>n</jats:italic> components. A strong size level is a subset of the form <jats:italic>σ</jats:italic> <jats:sup>−1</jats:sup>(<jats:italic>t</jats:italic>), where <jats:italic>σ</jats:italic> is a strong size map for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) and <jats:italic>t</jats:italic> ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each <jats:italic>n</jats:italic> ≥ 2, no strong size level for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) is irreducible.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Irreducibility of strong size levels\",\"authors\":\"Alejandro Illanes, Verónica Martínez-de-la-Vega\",\"doi\":\"10.1515/ms-2024-0039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a continuum <jats:italic>X</jats:italic>, <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) denotes the hyperspace of nonempty closed subsets of <jats:italic>X</jats:italic> with at most <jats:italic>n</jats:italic> components. A strong size level is a subset of the form <jats:italic>σ</jats:italic> <jats:sup>−1</jats:sup>(<jats:italic>t</jats:italic>), where <jats:italic>σ</jats:italic> is a strong size map for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) and <jats:italic>t</jats:italic> ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each <jats:italic>n</jats:italic> ≥ 2, no strong size level for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) is irreducible.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/ms-2024-0039\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/ms-2024-0039","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
给定一个连续体 X，Cn (X) 表示最多有 n 个分量的 X 的非空封闭子集的超空间。强大小层是形式为 σ -1(t) 的子集，其中 σ 是 Cn (X) 的强大小映射，t∈ (0, 1]。在本文中，为了回答 Capulín-Pérez、Fuentes-Montes de Oca、Lara-Mejía 和 Orozco-Zitli 提出的问题，我们证明了对于每个 n ≥ 2，Cn (X) 的强大小层次都是不可还原的。
Given a continuum X, Cn(X) denotes the hyperspace of nonempty closed subsets of X with at most n components. A strong size level is a subset of the form σ−1(t), where σ is a strong size map for Cn(X) and t ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each n ≥ 2, no strong size level for Cn(X) is irreducible.
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