Weak continuity and almost continuity
Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171284000338 |
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| _version_ | 1832563092425277440 |
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| author | D. A. Rose |
| author_facet | D. A. Rose |
| author_sort | D. A. Rose |
| collection | DOAJ |
| description | Two relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended. |
| format | Article |
| id | doaj-art-74d0f6b2afe1421296d4782d48556530 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-74d0f6b2afe1421296d4782d485565302025-02-03T01:20:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017231131810.1155/S0161171284000338Weak continuity and almost continuityD. A. Rose0Department of Mathematics, Francis Marion College, Florence, South Carolina 29501, USATwo relationships considered by Weston [1] for a pair of topologies on a set X are translated to a function setting. An attempt to characterize the two resulting types of functions leads to new characterizations of weak continuity and almost continuity. After showing that weak continuity and almost continuity are independent, interrelationships are sought. This leads to the definition of subweak continuity and a new characterization for almost openness. Finally, several published results are strengthened or slightly extended.http://dx.doi.org/10.1155/S0161171284000338weakly continuous functionalmost continuous functionsubweakly continuous function. |
| spellingShingle | D. A. Rose Weak continuity and almost continuity International Journal of Mathematics and Mathematical Sciences weakly continuous function almost continuous function subweakly continuous function. |
| title | Weak continuity and almost continuity |
| title_full | Weak continuity and almost continuity |
| title_fullStr | Weak continuity and almost continuity |
| title_full_unstemmed | Weak continuity and almost continuity |
| title_short | Weak continuity and almost continuity |
| title_sort | weak continuity and almost continuity |
| topic | weakly continuous function almost continuous function subweakly continuous function. |
| url | http://dx.doi.org/10.1155/S0161171284000338 |
| work_keys_str_mv | AT darose weakcontinuityandalmostcontinuity |