Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions
Two new classes of functions, called ‘almost z-supercontinuous functions’ and ’almost Dδ-supercontinuous functions’ are introduced. The class of almost z-supercontinuous functions properly includes the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33(7), (2002), 1097-1108) as well...
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2008-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1804 |
| _version_ | 1819240440350638080 |
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| author | J.K. Kohli D. Singh Rajesh Kumar |
| author_facet | J.K. Kohli D. Singh Rajesh Kumar |
| author_sort | J.K. Kohli |
| collection | DOAJ |
| description | Two new classes of functions, called ‘almost z-supercontinuous functions’ and ’almost Dδ-supercontinuous functions’ are introduced. The class of almost z-supercontinuous functions properly includes the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33(7), (2002), 1097-1108) as well as the class of almost clopen maps due to Ekici (Acta. Math. Hungar. 107(3), (2005), 193-206) and is properly contained in the class of almost Dδ-supercontinuous functions which in turn constitutes a proper subclass of the class of almost strongly θ-continuous functions due to Noiri and Kang (Indian J. Pure Appl. Math. 15(1), (1984), 1-8) and which in its turn include all δ-continuous functions of Noiri (J. Korean Math. Soc. 16 (1980), 161-166). Characterizations and basic properties of almost z-supercontinuous functions and almost Dδ-supercontinuous functions are discussed and their place in the hierarchy of variants of continuity is elaborated. Moreover, properties of almost strongly θ-continuous functions are investigated and sufficient conditions for almost strongly θ-continuous functions to have u θ-closed (θ-closed) graph are formulated. |
| first_indexed | 2024-12-23T14:08:03Z |
| format | Article |
| id | doaj.art-88e2f18a040b4a2fb955cb8567b731ed |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-12-23T14:08:03Z |
| publishDate | 2008-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-88e2f18a040b4a2fb955cb8567b731ed2022-12-21T17:44:08ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472008-10-019223925110.4995/agt.2008.18041462Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functionsJ.K. Kohli0D. Singh1Rajesh Kumar2University of DelhiUniversity of DelhiUniversity of DelhiTwo new classes of functions, called ‘almost z-supercontinuous functions’ and ’almost Dδ-supercontinuous functions’ are introduced. The class of almost z-supercontinuous functions properly includes the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33(7), (2002), 1097-1108) as well as the class of almost clopen maps due to Ekici (Acta. Math. Hungar. 107(3), (2005), 193-206) and is properly contained in the class of almost Dδ-supercontinuous functions which in turn constitutes a proper subclass of the class of almost strongly θ-continuous functions due to Noiri and Kang (Indian J. Pure Appl. Math. 15(1), (1984), 1-8) and which in its turn include all δ-continuous functions of Noiri (J. Korean Math. Soc. 16 (1980), 161-166). Characterizations and basic properties of almost z-supercontinuous functions and almost Dδ-supercontinuous functions are discussed and their place in the hierarchy of variants of continuity is elaborated. Moreover, properties of almost strongly θ-continuous functions are investigated and sufficient conditions for almost strongly θ-continuous functions to have u θ-closed (θ-closed) graph are formulated.http://polipapers.upv.es/index.php/AGT/article/view/1804(almost) z-supercontinuous function(almost) Dδ-supercontinuous function(almost) strongly θ-continuous functionAlmost continuous functionδ-continuous functionfaintly continuous functionuθ-closed graphθ-closed graphuθ-limit pointθ-limit po |
| spellingShingle | J.K. Kohli D. Singh Rajesh Kumar Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions Applied General Topology (almost) z-supercontinuous function (almost) Dδ-supercontinuous function (almost) strongly θ-continuous function Almost continuous function δ-continuous function faintly continuous function uθ-closed graph θ-closed graph uθ-limit point θ-limit po |
| title | Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions |
| title_full | Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions |
| title_fullStr | Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions |
| title_full_unstemmed | Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions |
| title_short | Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions |
| title_sort | generalizations of z supercontinuous functions and dδ supercontinuous functions |
| topic | (almost) z-supercontinuous function (almost) Dδ-supercontinuous function (almost) strongly θ-continuous function Almost continuous function δ-continuous function faintly continuous function uθ-closed graph θ-closed graph uθ-limit point θ-limit po |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1804 |
| work_keys_str_mv | AT jkkohli generalizationsofzsupercontinuousfunctionsandddsupercontinuousfunctions AT dsingh generalizationsofzsupercontinuousfunctionsandddsupercontinuousfunctions AT rajeshkumar generalizationsofzsupercontinuousfunctionsandddsupercontinuousfunctions |