Semi separation axioms and hyperspaces

Charles Dorsett

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-6

Abstract:

In this paper examples are given to show that s -regular and s -normal are independent; that s -normal, and s -regular are not semi topological properties; and that ( S ( X ) , E ( X ) ) need not be semi- T 1 even if ( X , T ) is compact, s -normal, s -regular, semi- T 2 , and T 0 . Also, it is shown that for each space ( X , T ) , ( S ( X ) , E ( X ) ) , ( S ( X 0 ) , E ( X 0 ) ) , and ( S ( X S 0 ) , E ( X S 0 ) ) are homeomorphic, where ( X 0 , Q ( X 0 ) ) is the T 0 -identification space of ( X , T ) and ( X S 0 , Q ( X S 0 ) ) is the semi- T 0 -identification space of ( X , T ) , and that if ( X , T ) is s -regular and R 0 , then ( S ( X ) , E ( X ) ) is semi- T 2 .

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:923796

DOI: 10.1155/S0161171281000318

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