Conditionally Evenly Convex Sets and Evenly Quasi-Convex Maps
  Evenly convex sets in a topological vector space are defined as the intersection of a family of open half spaces. We introduce a generalization of this concept in the conditional framework and provide a generalized version of the bipolar theorem. This notion is then applied to obtain the dual representation of conditionally evenly quasi-convex maps. 
Marco Frittelli and Marco Maggis
math.PR math.FA