Definition and characterisation
Let be an ordered set. is called a lattice if and only if any two elements have both a join and a meet.
Definition (algebraic lattice):
Let be any set, and let and be two functions. is called an algebraic lattice if and only if the functions and satisfy the following: For all
Special types of lattices
Definition (complete lattice):
A complete lattice is an ordered set such that whenever is a family of elements of , both and exist.