Semi-topological properties
A property preserved under a semi-homeomorphism is said to be a semi-topological property. In the present paper we prove the following results: (1) A topological property P is semi-topological if and only if the statement (X,𝒯) has P if and only if (X,F(𝒯)) has P′ is true where F(𝒯) is the finest to...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000346 |
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| _version_ | 1832566750358536192 |
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| author | Bhamini M. P. Nayar S. P. Arya |
| author_facet | Bhamini M. P. Nayar S. P. Arya |
| author_sort | Bhamini M. P. Nayar |
| collection | DOAJ |
| description | A property preserved under a semi-homeomorphism is said to be a semi-topological property. In the present paper we prove the following results: (1) A topological property P is semi-topological if and only if the statement (X,𝒯) has P if and only if (X,F(𝒯)) has P′ is true where F(𝒯) is the finest topology on X having the same family of semi-open sets as (X,𝒯), (2) If P is a topological property being minimal P is semi-topological if and only if for each minimal P space (X,𝒯), 𝒯=F(𝒯). |
| format | Article |
| id | doaj-art-42356531bd0e4d2680d00e710e567b8a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1992-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-42356531bd0e4d2680d00e710e567b8a2025-02-03T01:03:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115226727210.1155/S0161171292000346Semi-topological propertiesBhamini M. P. Nayar0S. P. Arya1Department of Mathematics, Howard University, Washington. DC 20059, USADepartment of Mathematics, Howard University, Washington. DC 20059, USAA property preserved under a semi-homeomorphism is said to be a semi-topological property. In the present paper we prove the following results: (1) A topological property P is semi-topological if and only if the statement (X,𝒯) has P if and only if (X,F(𝒯)) has P′ is true where F(𝒯) is the finest topology on X having the same family of semi-open sets as (X,𝒯), (2) If P is a topological property being minimal P is semi-topological if and only if for each minimal P space (X,𝒯), 𝒯=F(𝒯).http://dx.doi.org/10.1155/S0161171292000346semi-open setssemi-continuoussemi-homeomorphismsemi-topologicalminimal P-spaces. |
| spellingShingle | Bhamini M. P. Nayar S. P. Arya Semi-topological properties International Journal of Mathematics and Mathematical Sciences semi-open sets semi-continuous semi-homeomorphism semi-topological minimal P-spaces. |
| title | Semi-topological properties |
| title_full | Semi-topological properties |
| title_fullStr | Semi-topological properties |
| title_full_unstemmed | Semi-topological properties |
| title_short | Semi-topological properties |
| title_sort | semi topological properties |
| topic | semi-open sets semi-continuous semi-homeomorphism semi-topological minimal P-spaces. |
| url | http://dx.doi.org/10.1155/S0161171292000346 |
| work_keys_str_mv | AT bhaminimpnayar semitopologicalproperties AT sparya semitopologicalproperties |