  By considering the general properties of approximate units in differentiable
algebras, we are able to present a unified approach to characterising
completeness of spectral metric spaces, existence of connections on modules,
and the lifting of Kasparov products to the unbounded category. In particular,
by strengthening Kasparov's technical theorem, we show that given any two
composable KK-classes, we can find unbounded representatives whose product can
be constructed to yield an unbounded representative of the Kasparov product.
