On the Continuous Representation of Quasiconcave Functions by Their Upper Level Sets

We provide a continuous representation of quasiconcave functions by their upper level sets. A possible motivation is the extension to quasiconcave functions of a result by D. H. Hyers and S. M. Ulam [Proc. Amer. Math. Soc. 3(5) (1952) 821–828], which states that every approximately convex function can be approximated by a convex function.