  In this paper we establish a direct connection between stable approximate
unitary equivalence for $*$-homomorphisms and the topology of the KK-groups
which avoids entirely C*-algebra extension theory and does not require
nuclearity assumptions. To this purpose we show that a topology on the Kasparov
groups can be defined in terms of approximate unitary equivalence for Cuntz
pairs and that this topology coincides with both Pimsner's topology and the
Brown-Salinas topology. We study the generalized R{\o}rdam group
$KL(A,B)=KK(A,B)/\bar{0}$, and prove that if a separable exact residually
finite dimensional C*-algebra satisfies the universal coefficient theorem in
KK-theory, then it embeds in the UHF algebra of type $2^\infty$.
  In particular such an embedding exists for the C*-algebra of a second
countable amenable locally compact maximally almost periodic group.
