We investigate basic properties of the set of observer-based state-space compensators (OBCs). In particular, we are interested in how much of this set is occupied by its OBC members. We examine both classical OBCs and generalized OBCs, as developed in [D. Cobb, SIAM J. Control Optim., 50 (2012), pp. 1921-1949]. We perform our analysis for both real and complex compensators. In every case, we show that the set of OBCs is not open but has dense interior.