2021/07/07 by Frank a Campo, Campo, Frank a
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Topology and Set Theory #Advanced Optimization Algorithms Research
paper · pdf · doi:10.48550/arxiv.2107.03122
For a connected finite poset P, let E(P) be the poset induced by the\nextremal points of P. We show that the fixed point property of E(P) implies\nthe fixed point property of P. On the other hand, we show that a homomorphism\nf : E(P) \→ Q can be extended to P if Q is a flat poset not\ncontaining a 4-crown. We conclude that every retract-crown of E(P) with more\nthan four points is a retract-crown of P, too. We see that for P having the\nfixed point property but E(P) not, every edge of every crown in E(P) must\nbelong to a so-called improper 4-crown, with additional specifications if P\nhas height two. The results provide several sufficient and necessary conditions\nfor P having the fixed point property, and these conditions refer to objects\nsimpler than P.\n