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.
Fenecios, J. P., & Cabral, E. A. (2013). Left Baire-1 compositors and continuous functions. International Journal of Mathematics and Mathematical Sciences, 2013.