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:	Jonald P. Fenecios, Emmanuel A. Cabral
Format:	Article
Language:	English
Published:	Hindawi Limited 2013-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Online Access:	http://dx.doi.org/10.1155/2013/878253

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spelling	doaj-588fb3bfd4cf4c3dbfcac398915fe7ea2020-11-24T21:10:48ZengHindawi LimitedInternational 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
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jonald P. Fenecios Emmanuel A. Cabral
spellingShingle	Jonald P. Fenecios Emmanuel A. Cabral Left Baire-1 Compositors and Continuous Functions International Journal of Mathematics and Mathematical Sciences
author_facet	Jonald P. Fenecios Emmanuel A. Cabral
author_sort	Jonald P. Fenecios
title	Left Baire-1 Compositors and Continuous Functions
title_short	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_sort	left baire-1 compositors and continuous functions
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	2013-01-01
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.
url	http://dx.doi.org/10.1155/2013/878253
work_keys_str_mv	AT jonaldpfenecios leftbaire1compositorsandcontinuousfunctions AT emmanuelacabral leftbaire1compositorsandcontinuousfunctions
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Left Baire-1 Compositors and Continuous Functions

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