Locally closed sets and LC-continuous functions
In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the inters...
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| Format: | Article |
| Language: | English |
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Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289000505 |
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| _version_ | 1849308793479888896 |
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| author | M. Ganster I. L. Reilly |
| author_facet | M. Ganster I. L. Reilly |
| author_sort | M. Ganster |
| collection | DOAJ |
| description | In this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a
topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions. |
| format | Article |
| id | doaj-art-17a87e9f38be4e43ba7b23bef7119918 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-17a87e9f38be4e43ba7b23bef71199182025-08-20T03:54:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112341742410.1155/S0161171289000505Locally closed sets and LC-continuous functionsM. Ganster0I. L. Reilly1Department of Mathematics, University of California, Davis, California 95616, USADepartment of Mathematics, University of California, Davis, California 95616, USAIn this paper we introduce and study three different notions of generalized continuity, namely LC-irresoluteness, LC-continuity and sub-LC-continuity. All three notions are defined by using the concept of a locally closed set. A subset S of a topological space X is locally closed if it is the intersection of an open and a closed set. We discuss some properties of these functions and show that a function between topological spaces is continuous if and only if it is sub-LC-continuous and nearly continuous in the sense of Ptak. Several examples are provided to illustrate the behavior of these new classes of functions.http://dx.doi.org/10.1155/S0161171289000505 |
| spellingShingle | M. Ganster I. L. Reilly Locally closed sets and LC-continuous functions International Journal of Mathematics and Mathematical Sciences |
| title | Locally closed sets and LC-continuous functions |
| title_full | Locally closed sets and LC-continuous functions |
| title_fullStr | Locally closed sets and LC-continuous functions |
| title_full_unstemmed | Locally closed sets and LC-continuous functions |
| title_short | Locally closed sets and LC-continuous functions |
| title_sort | locally closed sets and lc continuous functions |
| url | http://dx.doi.org/10.1155/S0161171289000505 |
| work_keys_str_mv | AT mganster locallyclosedsetsandlccontinuousfunctions AT ilreilly locallyclosedsetsandlccontinuousfunctions |