On the relationship between classical and computable topology

In this talk, we will look at some important concepts in classical topology, and discuss their computable counterparts. The main goals are to combine many important results which are scattered throughout the literature, and to -nd the most natural de-nitions for computable versions of classical properties. It turns out that many notions in computable topology coincide more closely with the corresponding notion in limit/sequential spaces than the classical topological notion. Further, for the class of spaces admitting an admissible representation, in many cases the de-nitions coincide; an important case are the various topologies on the open sets, including the Scott topology.