Two general kinds of subsets of a partially ordered set P are always retracts of P: (1) every maximal chain of P is a retract; (2) in P, every isometric, spanning subset of length one with no crowns is a retract. It follows that in a partially ordered set P with the fixed point property, every maximal chain of P is complete and every isometric, spanning fence of P is finite.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics