Characterization of R-Evenly Quasiconvex Functions

A function defined on a locally convex space is called evenly quasiconvex if its level sets are intersections of families of open half-spaces. Furthermore, if the closures of these open halfspaces do not contain the origin, then the function is called R-evenly quasiconvex. In this note, R-evenly quasiconvex functions are characterized as those evenly-quasiconvex functions that satisfy a certain simple relation with their lower semicontinuous hulls.