Lattices of Lipschitz functions. Pacific J.
Math. 164 (1994), 179-193.
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(M) and its relation to M. We find that there is a nice duality between
M and Lip(M) (as a lattice). We also give an abstract classification of all
normed vector lattices which are isomorphic to Lip(M) for some M.
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