  The paper deals with the interplay between boundedness, order and ring
structures in function lattices on the line and related metric spaces. It is
shown that the lattice of all Lipschitz functions on a normed space $E$ is
isomorphic to its sublattice of bounded functions if and only if $E$ has
dimension one. The lattice of Lipschitz functions on $E$ carries a "hidden"
$f$-ring structure with a unit, and the same happens to the (larger) lattice of
all uniformly continuous functions for a wide variety of metric spaces.
  An example of a metric space whose lattice of uniformly continuous functions
supports no unital $f$-ring structure is provided.
