{"title":"Infinitary Noetherian constructions II. Transfinite words and the regular subword topology","authors":"J. Goubault-Larrecq, Simon Halfon, Aliaume Lopez","doi":"10.4064/cm8793-3-2023","DOIUrl":null,"url":null,"abstract":"We show that the spaces of transfinite words, namely ordinal-indexed words, over a Noetherian space, is also Noetherian, under a natural topology which we call the regular subword topology. We characterize its sobrification and its specialization ordering, and we give an upper bound on its dimension and on its stature.","PeriodicalId":49216,"journal":{"name":"Colloquium Mathematicum","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Colloquium Mathematicum","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/cm8793-3-2023","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We show that the spaces of transfinite words, namely ordinal-indexed words, over a Noetherian space, is also Noetherian, under a natural topology which we call the regular subword topology. We characterize its sobrification and its specialization ordering, and we give an upper bound on its dimension and on its stature.
期刊介绍：
Colloquium Mathematicum is a journal devoted to the publication of original papers of moderate length addressed to a broad mathematical audience. It publishes results of original research, interesting new proofs of important theorems and research-expository papers in all fields of pure mathematics.
Two issues constitute a volume, and at least four volumes are published each year.
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