  Let $\mathfrak{h}_3$ be the Heisenberg algebra and let $\mathfrak g$ be the
3-dimensional Lie algebra having $[e_1,e_2]=e_1\,(=-[e_2,e_1])$ as its only
non-zero commutation relations. We describe the closure of the orbit of a
vector of structure constants corresponding to $\mathfrak{h}_3$ and $\mathfrak
g$ respectively as an algebraic set giving in each case a set of polynomials
for which the orbit closure is the set of common zeros. Working over an
arbitrary infinite field, this description enables us to give an alternative
way, using the definition of an irreducible algebraic set, of obtaining all
degenerations of $\mathfrak{h}_3$ and $\mathfrak g$ (the degeneration from
$\mathfrak g$ to $\mathfrak{h}_3$ being one of them).
