3. Mathematical formalisms

Set and function theory, used directly in the previous section, provides a first formal framework for mathematical morphology. The most general framework, for increasing deterministic operations, is the algebraic framework of complete lattices. A lattice is a set $\mathcal{T}$ with a partial order relation $\le$ , such that any pair of elements (or any finite family) has an upper bound (denoted $x\vee y$ ) and a lower bound (denoted