Title

Some characterizations of pseudo-chains in pseudo-ordered sets.

Authors

Rai, Shashirekha B.; Bhatta, S. Parameshwara

Abstract

In this paper, we have proved that minimum condition in a pseudo-ordered set (psoset) is equivalent to the descending pseudo-chain condition. Characterization of a pseudo-chain in an acyclic psoset is obtained using graph theoretic approach as transitivity need not hold in psosets. Skala proved that every complete trellis has Fixed Point Property. A counterexample given in this paper shows that trellis having Fixed Point Property need not be complete. The notion of weakly isotone mapping and Strong Fixed Point Property is introduced in a psoset and the characterization of weakly isotone mapping is obtained. It is proved that a connected psoset containing a nontrivial cycle does not have Strong Fixed Point Property.

Subjects

ORDERED sets; MAXIMA & minima

Publication

Asian-European Journal of Mathematics, 2021, Vol 14, Issue 5, pN.PAG

ISSN

1793-5571

Publication type

Academic Journal

DOI

10.1142/S1793557121500741