{"title":"The Absolutely Strongly Star-Hurewicz Property with Respect to an Ideal","authors":"Sumit Singh, B. Tyagi, M. Bhardwaj","doi":"10.2478/tmmp-2020-0020","DOIUrl":null,"url":null,"abstract":"Abstract Aspace X is said to have the absolutely strongly star --Hurewicz (ASSH) property if for each sequence (𝒰n : n ∈ )of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ ) of finite subsets of Y such that for each x ∈ X, {n ∈ : x ∉ St(Fn, 𝒰n)}∈ , where is the proper admissible ideal of . In this paper, we investigate the relationship between the ASSH property and other related properties and study the topological properties of the ASSH property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASSH properties.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"76 1","pages":"81 - 94"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tatra Mountains Mathematical Publications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2478/tmmp-2020-0020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract Aspace X is said to have the absolutely strongly star --Hurewicz (ASSH) property if for each sequence (𝒰n : n ∈ )of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ ) of finite subsets of Y such that for each x ∈ X, {n ∈ : x ∉ St(Fn, 𝒰n)}∈ , where is the proper admissible ideal of . In this paper, we investigate the relationship between the ASSH property and other related properties and study the topological properties of the ASSH property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASSH properties.
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