Semi separation axioms and hyperspaces
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-T1 even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T)...
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| Format: | Article |
| Language: | English |
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Wiley
1981-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171281000318 |
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| _version_ | 1832562670845296640 |
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| author | Charles Dorsett |
| author_facet | Charles Dorsett |
| author_sort | Charles Dorsett |
| collection | DOAJ |
| description | 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-T1 even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X),E(X)), (S(X0),E(X0)), and (S(XS0),E(XS0)) are homeomorphic, where (X0,Q(X0)) is the T0-identification space of (X,T) and (XS0,Q(XS0)) is the semi-T0-identification space of (X,T), and that if (X,T) is s-regular and R0, then (S(X),E(X)) is semi-T2. |
| format | Article |
| id | doaj-art-61a04f4e2046415ea49d69c072c5180b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1981-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-61a04f4e2046415ea49d69c072c5180b2025-02-03T01:22:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251981-01-014344545010.1155/S0161171281000318Semi separation axioms and hyperspacesCharles Dorsett0Department of Mathematics, Texas A&M University, College Station, Texas, USAIn 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-T1 even if (X,T) is compact, s-normal, s-regular, semi-T2, and T0. Also, it is shown that for each space (X,T), (S(X),E(X)), (S(X0),E(X0)), and (S(XS0),E(XS0)) are homeomorphic, where (X0,Q(X0)) is the T0-identification space of (X,T) and (XS0,Q(XS0)) is the semi-T0-identification space of (X,T), and that if (X,T) is s-regular and R0, then (S(X),E(X)) is semi-T2.http://dx.doi.org/10.1155/S0161171281000318semi open setssemi topological propertiesand hyperspaces. |
| spellingShingle | Charles Dorsett Semi separation axioms and hyperspaces International Journal of Mathematics and Mathematical Sciences semi open sets semi topological properties and hyperspaces. |
| title | Semi separation axioms and hyperspaces |
| title_full | Semi separation axioms and hyperspaces |
| title_fullStr | Semi separation axioms and hyperspaces |
| title_full_unstemmed | Semi separation axioms and hyperspaces |
| title_short | Semi separation axioms and hyperspaces |
| title_sort | semi separation axioms and hyperspaces |
| topic | semi open sets semi topological properties and hyperspaces. |
| url | http://dx.doi.org/10.1155/S0161171281000318 |
| work_keys_str_mv | AT charlesdorsett semiseparationaxiomsandhyperspaces |