{"title":"On $n$-dimensional Niemytzki spaces","authors":"Vitalij A. Chatyrko","doi":"arxiv-2405.02708","DOIUrl":null,"url":null,"abstract":"In this paper we extend the construction of the Niemytzki plane to dimension\n$n \\geq 3$ and explore some properties of the new spaces. Furthermore, we\nconsider a poset of topologies on the closed $n$-dimensional Euclidean\nhalf-space similar to one from \\cite{AAK} which is related to the Niemytzki\nplane topology.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"62 1","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":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2405.02708","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we extend the construction of the Niemytzki plane to dimension
$n \geq 3$ and explore some properties of the new spaces. Furthermore, we
consider a poset of topologies on the closed $n$-dimensional Euclidean
half-space similar to one from \cite{AAK} which is related to the Niemytzki
plane topology.
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