Maximizing a Binary Relation on Compact Subsets
Nikolai S. Kukushkin · 2006
The sets of maximal elements of a binary relation on compact subsets of a metric space deflne a choice function. Possibilities to characterize natural properties of the choice function (path independence, nonempty values, closed values, etc.) by algebraic and topological conditions on the underlying relation are investigated. The latter are formulated in terms of \conflgurations realizable or not for the relation. The existence of maximal elements on all compact subsets exceeds every other property in the complexity of conditions needed for its characterization.