 A sublattice of a vector lattice "X" is a vector subspace "M" of "X" such that for all "x" and "y" in "M", sup"X"("x", "y") belongs to "X" (importantly, note that this supremum is taken in "X" and not in "M").If "X" = formula_62 with 0 < p < 1, then the 2-dimensional vector subspace "M" of "X" defined by all maps of the form formula_63 ("a", "b" ∈ formula_1) is a vector lattice under the induced order but is "not" a sublattice of "X".This despite "X" being an order complete Archimedean ordered topological vector lattice.