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International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 878253, 3 pages
http://dx.doi.org/10.1155/2013/878253
Research Article

Left Baire-1 Compositors and Continuous Functions

1Department of Mathematics, Ateneo de Davao University, E. Jacinto Street, 8000 Davao City, Philippines
2Department 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 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 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.