  We extend the Luzin hierarchy of qcb$_0$-spaces introduced in [ScS13] to all
countable ordinals, obtaining in this way the hyperprojective hierarchy of
qcb$_0$-spaces. We generalize all main results of [ScS13] to this larger
hierarchy. In particular, we extend the Kleene-Kreisel continuous functionals
of finite types to the continuous functionals of countable types and relate
them to the new hierarchy. We show that the category of hyperprojective
qcb$_0$-spaces has much better closure properties than the category of
projective qcb$_0$-space. As a result, there are natural examples of spaces
that are hyperprojective but not projective.
