Between strong continuity and almost continuity
As embodied in the title of the paper strong and weak variants of continuity that lie strictly between strong continuity of Levine and almost continuity due to Singal and Singal are considered. Basic properties of almost completely continuous functions (≡ R-maps) and δ-continuous functions are studi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Universitat Politècnica de València
2010-04-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1726 |
| _version_ | 1828331399078215680 |
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| author | J.K. Kohli D. Singh |
| author_facet | J.K. Kohli D. Singh |
| author_sort | J.K. Kohli |
| collection | DOAJ |
| description | As embodied in the title of the paper strong and weak variants of continuity that lie strictly between strong continuity of Levine and almost continuity due to Singal and Singal are considered. Basic properties of almost completely continuous functions (≡ R-maps) and δ-continuous functions are studied. Direct and inverse transfer of topological properties under almost completely continuous functions and δ-continuous functions are investigated and their place in the hier- archy of variants of continuity that already exist in the literature is out- lined. The class of almost completely continuous functions lies strictly between the class of completely continuous functions studied by Arya and Gupta (Kyungpook Math. J. 14 (1974), 131-143) and δ-continuous functions defined by Noiri (J. Korean Math. Soc. 16, (1980), 161-166). The class of almost completely continuous functions properly contains each of the classes of (1) completely continuous functions, and (2) al- most perfectly continuous (≡ regular set connected) functions defined by Dontchev, Ganster and Reilly (Indian J. Math. 41 (1999), 139-146) and further studied by Singh (Quaestiones Mathematicae 33(2)(2010), 1–11) which in turn include all δ-perfectly continuous functions initi- ated by Kohli and Singh (Demonstratio Math. 42(1), (2009), 221-231) and so include all perfectly continuous functions introduced by Noiri (Indian J. Pure Appl. Math. 15(3) (1984), 241-250). |
| first_indexed | 2024-04-13T20:52:00Z |
| format | Article |
| id | doaj.art-9528c08ad9944ad1ba3987a9c282d756 |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-13T20:52:00Z |
| publishDate | 2010-04-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-9528c08ad9944ad1ba3987a9c282d7562022-12-22T02:30:28ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472010-04-01111294210.4995/agt.2010.17261414Between strong continuity and almost continuityJ.K. Kohli0D. Singh1University of DelhiUniversity of DelhiAs embodied in the title of the paper strong and weak variants of continuity that lie strictly between strong continuity of Levine and almost continuity due to Singal and Singal are considered. Basic properties of almost completely continuous functions (≡ R-maps) and δ-continuous functions are studied. Direct and inverse transfer of topological properties under almost completely continuous functions and δ-continuous functions are investigated and their place in the hier- archy of variants of continuity that already exist in the literature is out- lined. The class of almost completely continuous functions lies strictly between the class of completely continuous functions studied by Arya and Gupta (Kyungpook Math. J. 14 (1974), 131-143) and δ-continuous functions defined by Noiri (J. Korean Math. Soc. 16, (1980), 161-166). The class of almost completely continuous functions properly contains each of the classes of (1) completely continuous functions, and (2) al- most perfectly continuous (≡ regular set connected) functions defined by Dontchev, Ganster and Reilly (Indian J. Math. 41 (1999), 139-146) and further studied by Singh (Quaestiones Mathematicae 33(2)(2010), 1–11) which in turn include all δ-perfectly continuous functions initi- ated by Kohli and Singh (Demonstratio Math. 42(1), (2009), 221-231) and so include all perfectly continuous functions introduced by Noiri (Indian J. Pure Appl. Math. 15(3) (1984), 241-250).http://polipapers.upv.es/index.php/AGT/article/view/1726(almost) z-supercontinuous function(almost) Dδ -supercontinuous function(almost) strongly θ-continuous function(almost) completely continuous functionnearly paracompact spacealmost partition topology |
| spellingShingle | J.K. Kohli D. Singh Between strong continuity and almost continuity Applied General Topology (almost) z-supercontinuous function (almost) Dδ -supercontinuous function (almost) strongly θ-continuous function (almost) completely continuous function nearly paracompact space almost partition topology |
| title | Between strong continuity and almost continuity |
| title_full | Between strong continuity and almost continuity |
| title_fullStr | Between strong continuity and almost continuity |
| title_full_unstemmed | Between strong continuity and almost continuity |
| title_short | Between strong continuity and almost continuity |
| title_sort | between strong continuity and almost continuity |
| topic | (almost) z-supercontinuous function (almost) Dδ -supercontinuous function (almost) strongly θ-continuous function (almost) completely continuous function nearly paracompact space almost partition topology |
| url | http://polipapers.upv.es/index.php/AGT/article/view/1726 |
| work_keys_str_mv | AT jkkohli betweenstrongcontinuityandalmostcontinuity AT dsingh betweenstrongcontinuityandalmostcontinuity |