{"title":"哈恩函数对和单独的连续函数","authors":"O. Maslyuchenko, A. Kushnir","doi":"10.31861/bmj2021.01.18","DOIUrl":null,"url":null,"abstract":"In this paper we continue the study of interconnections between separately continuous\nfunction which was started by V. K. Maslyuchenko. A pair (g, h) of functions on a topological space is called a pair of Hahn if g ≤ h, g is an upper semicontinuous function and h is a lower semicontinuous function. We say that a pair of Hahn (g, h) is generated by a function f, which depends on two variables, if the infimum of f and the supremum of f with respect to the second variable equals g and h respectively. We prove that for any perfectly normal space X and non-pseudocompact space Y every pair of Hahn on X is generated by a continuous function on X x Y . We also obtain that for any perfectly normal space X and for any space Y having non-scattered compactification any pair of Hahn on X is generated by a separately continuous function on X x Y .","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"PAIRS OF HAHN AND SEPARATELY CONTINUOUS FUNCTION\",\"authors\":\"O. Maslyuchenko, A. Kushnir\",\"doi\":\"10.31861/bmj2021.01.18\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we continue the study of interconnections between separately continuous\\nfunction which was started by V. K. Maslyuchenko. A pair (g, h) of functions on a topological space is called a pair of Hahn if g ≤ h, g is an upper semicontinuous function and h is a lower semicontinuous function. We say that a pair of Hahn (g, h) is generated by a function f, which depends on two variables, if the infimum of f and the supremum of f with respect to the second variable equals g and h respectively. We prove that for any perfectly normal space X and non-pseudocompact space Y every pair of Hahn on X is generated by a continuous function on X x Y . We also obtain that for any perfectly normal space X and for any space Y having non-scattered compactification any pair of Hahn on X is generated by a separately continuous function on X x Y .\",\"PeriodicalId\":196726,\"journal\":{\"name\":\"Bukovinian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bukovinian Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31861/bmj2021.01.18\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bukovinian Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31861/bmj2021.01.18","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
在本文中,我们继续研究由V. K. Maslyuchenko开始的独立连续函数之间的相互关系。如果g≤h,且g是上半连续函数,h是下半连续函数,则拓扑空间上的函数对(g, h)称为Hahn对。我们说一对Hahn (g, h)是由一个函数f生成的,它依赖于两个变量,如果f对第二个变量的最小值和最大值分别等于g和h。证明了对于任意完全正规空间X和非伪紧空间Y, X上的每一对哈恩函数都是由X X Y上的一个连续函数生成的。我们还得到了对于任何完全正规空间X和具有非分散紧化的空间Y, X上的任何哈恩函数对都是由X X Y上的一个单独的连续函数生成的。
In this paper we continue the study of interconnections between separately continuous
function which was started by V. K. Maslyuchenko. A pair (g, h) of functions on a topological space is called a pair of Hahn if g ≤ h, g is an upper semicontinuous function and h is a lower semicontinuous function. We say that a pair of Hahn (g, h) is generated by a function f, which depends on two variables, if the infimum of f and the supremum of f with respect to the second variable equals g and h respectively. We prove that for any perfectly normal space X and non-pseudocompact space Y every pair of Hahn on X is generated by a continuous function on X x Y . We also obtain that for any perfectly normal space X and for any space Y having non-scattered compactification any pair of Hahn on X is generated by a separately continuous function on X x Y .