Nelson Martins-Ferreira: Topological space objects via neighbourhood systems

In this talk we consider the problem of defining a topological space object internal to an arbitrary category (perhaps with some extra structure, or appropriate conditions) in such a way that a topological space object in the category SET, of sets and maps, is a topological space, while, for instance in the category of groups, it is a topological group. A solution via neighbourhood systems seems to be a good candidate. We would like to discuss this and other possibilities.