On the existence of maximal elements: An impossibility theorem

All sufficient (as well as necessary) conditions for a binary relation on a metric space to admit a maximal element on every nonempty compact subset of its domain that have been found so far in the literature can be expressed as the prohibition of certain "configurations." No condition of this form could be necessary and sufficient simultaneously.

• Type: Journal
• Year: 2008
• Where: DAM
• Authors: Nikolai S. Kukushkin
• Keywords: Binary Relation, DAM 2008, Maximal Element, Nonempty Compact Subset