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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |