Lattice isomorphisms between separation-property sublattices of C(X,I) and C(Y,I) induce homeomorphisms μ:Y→X; with multiplication closure they admit pointwise representation via strictly increasing maps on a dense Gδ set, and everywhere for Lipschitz functions on metric spaces.
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Lattice isomorphisms between certain sublattices of continuous functions
Lattice isomorphisms between separation-property sublattices of C(X,I) and C(Y,I) induce homeomorphisms μ:Y→X; with multiplication closure they admit pointwise representation via strictly increasing maps on a dense Gδ set, and everywhere for Lipschitz functions on metric spaces.