A comparison of continuously controlled and controlled K-theory

We define an unreduced version of the ε-controlled lower k-theoretic groups of Ranicki and Yamasaki (1995) and Quinn (1985). We show that the reduced versions of our groups coincide (in the inverse limit and its first derived, lim1) with those of Ranicki and Yamasaki. We also relate the controlled groups to the continuously controlled groups of Anderson and Munkholm (1994), and to the Quinn homology groups of Quinn (1982).