Representations of bipartite completed posets.
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
For a partially ordered set let us denote by the system of all convex subsets of . It is found the necessary and sufficient condition (concerning ) under which (as a partially ordered set) is selfdual.
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
This paper gives some new characterizations of completeness for trellises by introducing the notion of a cycle-complete trellis. One of our results yields, in particular, a characterization of completeness for trellises of finite length due to K. Gladstien (see K. Gladstien: Characterization of completeness for trellises of finite length, Algebra Universalis 3 (1973), 341–344).