  For a noncommutative space X, we study Inj(X), the set of isomorphism classes
of indecomposable injective X-modules. In particular, we look at how this set,
suitably topologized, can be viewed as an underlying "spectrum" for X. As
applications we discuss noncommutative notions of irreducibility and
integrality, and a way of associating an integral subspace of X to each element
of Inj(X) which behaves like a "weak point."
