Reduced Lattices

Abstract

Recall that a poset P is said to be a lattice if every two-point set {a, b} has a least upper bound a ∨ b, called join or supremum of a and b, and a greatest lower bound a ∧ b, called meet or infimum. Any finite lattice has a maximum (and a minimum), and in particular it is a contractible finite space. In this chapter we will study the spaces obtained from a lattice by removing its maximum and its minimum, which are more attractive from a topological point of view.