  We give a combinatorial characterization of countable submaximal subspaces of
$2^\kappa$. Using a parametrized version of Mathias forcing, we prove that
there exists a countable submaximal subspace of $2^{\omega_1}$ whilst
$\mathfrak{c}=\omega_2$. Combining this with previous results, we construct a
disjointly tight countable irresolvable space of weight $<\mathfrak{c}$,
answering a question of Bella and Hru\v{s}\'{a}k.
