Order- and Lattice-Structures

In this part we want to condense the new mathematical ideas and structures that have been introduced so far into a mathematical theory, which can be put in the framework of lattice theory. In the next chapter we want to get a better understanding of the order structure (defined in Definition 10.3 on the set of all covers. For this purpose we now introduce a number of basic concepts concerning order and lattices (Birkhoff 1967).