  We show that there exist (continuum many) varieties of bi-Heyting algebras
that are not generated by their complete members. It follows that there exist
(continuum many) extensions of the Heyting-Brouwer logic $\mathsf{HB}$ that are
topologically incomplete. This result provides further insight into the
long-standing open problem of Kuznetsov by yielding a negative solution of the
reformulation of the problem from intermediate logics to extensions of
$\mathsf{HB}$.
