INTERPRETATIONS OF THE GAP TOPOLOGY - A SURVEY

We explore the interconnections between various ways of introducing th e gap topology for linear time-invariant input/output systems. Specifi cally, we consider: 1. the topology defined by the gaps between the gr aphs of transfer functions 2. Vidyasagar's graph topology 3. the weake st topology in which the closed loop behavior of the standard feedback interconnection is continuous 4. the topology of uniform convergence of the associated Martin-Hermann mappings from C+ to the Grassmannian manifold Grass(m, m + p) ('pointwise gap') 5. the gap topology defined by the gaps between the associated L2(-infinity, 0)-behaviors. We als o compare some different gap topologies.