亚历山德罗夫空间的避让谱

Q2 Multidisciplinary

Universitas Scientiarum Pub Date : 2024-05-04 DOI:10.11144/javeriana.sc292.taso

Luis F. Mejías, J. E. Vielma

{"title":"亚历山德罗夫空间的避让谱","authors":"Luis F. Mejías, J. E. Vielma","doi":"10.11144/javeriana.sc292.taso","DOIUrl":null,"url":null,"abstract":"In this paper we prove that every T0 Alexandroff topological space (X, τ ) is homeomorphic to the avoidance of a subspace of (Spec(Λ), τZ), where Spec(Λ) denotes the prime spectrum of a semi-ring Λ induced by τ and τZ is the Zariski topology. We also prove that (Spec(Λ), τZ) is an Alexandroff space if and only if Λ satisfies the Gilmer property.","PeriodicalId":39200,"journal":{"name":"Universitas Scientiarum","volume":"50 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Avoidance Spectrum of Alexandroff Spaces\",\"authors\":\"Luis F. Mejías, J. E. Vielma\",\"doi\":\"10.11144/javeriana.sc292.taso\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we prove that every T0 Alexandroff topological space (X, τ ) is homeomorphic to the avoidance of a subspace of (Spec(Λ), τZ), where Spec(Λ) denotes the prime spectrum of a semi-ring Λ induced by τ and τZ is the Zariski topology. We also prove that (Spec(Λ), τZ) is an Alexandroff space if and only if Λ satisfies the Gilmer property.\",\"PeriodicalId\":39200,\"journal\":{\"name\":\"Universitas Scientiarum\",\"volume\":\"50 8\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Universitas Scientiarum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.11144/javeriana.sc292.taso\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Universitas Scientiarum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11144/javeriana.sc292.taso","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Multidisciplinary","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们证明了每个 T0 亚历山德罗夫拓扑空间（X, τ ）都与（Spec(Λ), τZ）的一个子空间的回避同构，其中 Spec(Λ) 表示由 τ 引起的半环Λ的素谱，τZ 是扎里斯基拓扑。我们还证明，只有当Λ满足吉尔默性质时，（Spec(Λ), τZ）才是亚历山大罗夫空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Avoidance Spectrum of Alexandroff Spaces

In this paper we prove that every T0 Alexandroff topological space (X, τ ) is homeomorphic to the avoidance of a subspace of (Spec(Λ), τZ), where Spec(Λ) denotes the prime spectrum of a semi-ring Λ induced by τ and τZ is the Zariski topology. We also prove that (Spec(Λ), τZ) is an Alexandroff space if and only if Λ satisfies the Gilmer property.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Universitas Scientiarum Multidisciplinary-Multidisciplinary

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

15 weeks