K-continuous Functions and Right B1 Compositors
A function g:R→R from the real line to itself is called a right B1 compositor if for any Baire class one function f:R→R,f◦g:R→R is Baire class one. In this study, we first apply Jayne-Rogers Theorem  to prove that every right B1 compositor is D-continuous where D is the class of all positive functions on R and thus give a positive answer to a problem posed by D. Zhao. This result then characterizes the right B1 compositor as a class of naturally defined functions. Furthermore, we also improved some of the results in . Lastly, a counter example was constructed to a claim in  that every function with a finite number of discontinuity points is left B1 compositor.
Fenecios, Jonald P., and Emmanuel A. Cabral. "K-continuous Functions and Right B1 Compositors." Journal of the Indonesian Mathematical Society, vol. 18, no. 1, 26 Apr. 2012, pp. 37-44.