Lattices of Lipschitz functions
Nikolai Weaver · Pacific Journal of Mathematics · 1994
Let M be a metric space.We observe that Lip(M) has a striking lattice structure: its closed unit ball is lattice-complete and completely distributive.This motivates further study into the lattice structure of Lip (A/) and its relation to M. We find that there is a nice duality between M and Lip(Λf) (as a lattice).We also give an abstract classification of all normed vector lattices which are isomorphic to Lip(M) for some M.