Existence of maximal elements of semicontinuous preorders
Gianni Bosi, Magalì E. Zuanon · International Journal of Mathematical Analysis · 2013
We discuss the existence of an upper semicontinuous multi-utility representation of a preorder on a topological space. We then prove that every weakly upper semicontinuous preorder is extended by an upper semicontinuous preorder and use this fact in order to show that every weakly upper semicontinuous preorder on a compact topological space admits a maximal element.