On barely continuous functions
The term barely continuous is a topological generalization of Baire-1 according to F. Gerlits of the Mathematical Institute of the Hungarian Academy of Sciences, and thus worthy of further study. This paper compares barely continuous functions and continuous functions on an elementary level. Knowing...
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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000845 |
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| _version_ | 1832561831987642368 |
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| author | Richard Stephens |
| author_facet | Richard Stephens |
| author_sort | Richard Stephens |
| collection | DOAJ |
| description | The term barely continuous is a topological generalization of Baire-1 according to F. Gerlits of the Mathematical Institute of the Hungarian Academy of Sciences, and thus worthy of further study. This paper compares barely continuous functions and continuous functions on an elementary level. Knowing how the continuity of the identity function between topologies on a given set yields the lattice structure for those topologies, the barely continuity of the identity function between topologies on a given set is investigated and used to add to the structure of that lattice. Included are certain sublattices generated by the barely continuity of the identity function between those topologies. Much attention is given to topologies on finite sets. |
| format | Article |
| id | doaj-art-441f964a51014d7d88f3890f55177963 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-441f964a51014d7d88f3890f551779632025-02-03T01:24:02ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-0111469569910.1155/S0161171288000845On barely continuous functionsRichard Stephens0Department of Applied Mathematics, Western Carolina University, Cullowhee 28723, NC, USAThe term barely continuous is a topological generalization of Baire-1 according to F. Gerlits of the Mathematical Institute of the Hungarian Academy of Sciences, and thus worthy of further study. This paper compares barely continuous functions and continuous functions on an elementary level. Knowing how the continuity of the identity function between topologies on a given set yields the lattice structure for those topologies, the barely continuity of the identity function between topologies on a given set is investigated and used to add to the structure of that lattice. Included are certain sublattices generated by the barely continuity of the identity function between those topologies. Much attention is given to topologies on finite sets.http://dx.doi.org/10.1155/S0161171288000845barely continuousbarely finerslightly finerbarely equivalentup latticedown latticebarely discrete. |
| spellingShingle | Richard Stephens On barely continuous functions International Journal of Mathematics and Mathematical Sciences barely continuous barely finer slightly finer barely equivalent up lattice down lattice barely discrete. |
| title | On barely continuous functions |
| title_full | On barely continuous functions |
| title_fullStr | On barely continuous functions |
| title_full_unstemmed | On barely continuous functions |
| title_short | On barely continuous functions |
| title_sort | on barely continuous functions |
| topic | barely continuous barely finer slightly finer barely equivalent up lattice down lattice barely discrete. |
| url | http://dx.doi.org/10.1155/S0161171288000845 |
| work_keys_str_mv | AT richardstephens onbarelycontinuousfunctions |