This lecture—based on the author's book, General Lattice Theory , Birkhäuser Verlag, 1978—briefly introduces the basic concepts of lattice theory, as needed for the lecture " Some combinatorial aspects of congruence lattice representations ". 1.1. Posets. A partially ordered set A; ≤≤ consists of a nonvoid set A and a binary relation ≤ on A such that the relation ≤ satisfies properties (P1)–(P3...

A Jbre F of a partially ordered set P is a subset which intersects each nontrivial maximal antichain of P. Let I be the smallest constant such that each finite partially ordered set P contains a fibre of size at most I ‘1 PI. We show that 1, < 3 by finding a good 3-coloring of the nontrivial antichains of P. Some decision problems involving iibres are also considered. For instance, it is shown ...

Set-valued ordered information systems can be classified into two categories: disjunctive and conjunctive systems. Through introducing two new dominance relations to set-valued information systems, we first introduce the conjunctive/disjunctive set-valued ordered information systems, and develop an approach to queuing problems for objects in presence of multiple attributes and criteria. Then, w...

A topology on a lattice L or more generally on a partially ordered set P is called an intrinsic topology if it is de ned directly from the order Early ex amples of such topologies were the interval topology of O Frink Fr and the order topology introduced by G Birkho Bi The early intrinsic topolo gies were typically symmetric i e the topology de ned on L agreed with the topology de ned on L the ...