Narrow Results

There is one-one correspondence between a subfamily of strong ideals and the family of strong congruences in a distributive and complemented generalised lattice.

$\chi$-Posets and $\chi$-lattices are generalizations of posets and lattices introduced by Juhani Nieminen, where $\chi$ denotes a choice function. In this paper, some new characterizations of $\chi$-lattices and $0,1$-posets are obtained.

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.