Before revision:  We firstly ] take a closer look at the mappings of various existing mapped WENO schemes and devise a general formula for them.
After revision:  We firstly ], the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long-run simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for the mapped WENO schemes. Thus, in our present work, we firstly define the family of the mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively take a closer look at the mappings of various existing mapped WENO schemes and devise a general formula for them.