On topological types of ordered median functions

Abstract

An ordered median functions is a continuous piecewise-linear function. It is well known that in finite dimensional spaces every continuous piecewise-linear function admits a max-min representation in terms of its linear functions. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones.

Keywords:

• ordered median functions
• max-min representation
• convex analysis

AMS Subject Classifications:

• 52A07
• 26B40
• 90B85