Left Baire-1 Compositors and Continuous Functions
We showed that the class of left Baire-1 compositors is precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative the conjecture in the work by Fenecios and Cabral (2012, page 43). Moreover, based on...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2013/878253 |
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| _version_ | 1832564122935361536 |
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| author | Jonald P. Fenecios Emmanuel A. Cabral |
| author_facet | Jonald P. Fenecios Emmanuel A. Cabral |
| author_sort | Jonald P. Fenecios |
| collection | DOAJ |
| description | We showed that the class of left Baire-1 compositors
is precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative
the conjecture in the work by Fenecios and Cabral (2012, page 43). Moreover, based on the above result
we provide a new proof that the class of functions ℬ𝒮,𝒯 where 𝒮 is the class of all positive continuous functions and 𝒯 is the class of all positive constants as defined in the work by Bakowska and Pawlak (2010) is exactly the class of all continuous functions. |
| format | Article |
| id | doaj-art-588fb3bfd4cf4c3dbfcac398915fe7ea |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-588fb3bfd4cf4c3dbfcac398915fe7ea2025-02-03T01:11:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252013-01-01201310.1155/2013/878253878253Left Baire-1 Compositors and Continuous FunctionsJonald P. Fenecios0Emmanuel A. Cabral1Department of Mathematics, Ateneo de Davao University, E. Jacinto Street, 8000 Davao City, PhilippinesDepartment of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, PhilippinesWe showed that the class of left Baire-1 compositors is precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao (2007, page 550) and settles in the affirmative the conjecture in the work by Fenecios and Cabral (2012, page 43). Moreover, based on the above result we provide a new proof that the class of functions ℬ𝒮,𝒯 where 𝒮 is the class of all positive continuous functions and 𝒯 is the class of all positive constants as defined in the work by Bakowska and Pawlak (2010) is exactly the class of all continuous functions.http://dx.doi.org/10.1155/2013/878253 |
| spellingShingle | Jonald P. Fenecios Emmanuel A. Cabral Left Baire-1 Compositors and Continuous Functions International Journal of Mathematics and Mathematical Sciences |
| title | Left Baire-1 Compositors and Continuous Functions |
| title_full | Left Baire-1 Compositors and Continuous Functions |
| title_fullStr | Left Baire-1 Compositors and Continuous Functions |
| title_full_unstemmed | Left Baire-1 Compositors and Continuous Functions |
| title_short | Left Baire-1 Compositors and Continuous Functions |
| title_sort | left baire 1 compositors and continuous functions |
| url | http://dx.doi.org/10.1155/2013/878253 |
| work_keys_str_mv | AT jonaldpfenecios leftbaire1compositorsandcontinuousfunctions AT emmanuelacabral leftbaire1compositorsandcontinuousfunctions |