Left Baire-1 Compositors and Continuous FunctionsReport as inadecuate




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International Journal of Mathematics and Mathematical SciencesVolume 2013 2013, Article ID 878253, 3 pages

Research Article

Department of Mathematics, Ateneo de Davao University, E. Jacinto Street, 8000 Davao City, Philippines

Department of Mathematics, Ateneo de Manila University, Loyola Heights, 1108 Quezon City, Philippines

Received 22 February 2013; Revised 23 September 2013; Accepted 26 September 2013

Academic Editor: Hernando Quevedo

Copyright © 2013 Jonald P. Fenecios and Emmanuel A. Cabral. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We showed that the class of left Baire-1 compositorsis precisely the class of continuous functions. This answers a characterization problem posed in the work by Zhao 2007, page 550 and settles in the affirmativethe conjecture in the work by Fenecios and Cabral 2012, page 43. Moreover, based on the above resultwe provide a new proof that the class of functions where is the class of all positive continuous functions and 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.





Author: Jonald P. Fenecios and Emmanuel A. Cabral

Source: https://www.hindawi.com/



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