Programme leaders: J.M. Aarts, J. van Mill
Dutch topology has a long tradition and enjoys an excellent international reputation. The work of the Dutch topologists covers all of General Topology and its connections with other disciplines. There are ongoing collaborations with distinguished researchers from Canada, the Czech Republic, Poland and the United States and the Dutch group plays an important role in the international organization of topological research.
In the current project various topological techniques are applied to topological dynamics (including topological groups), measure theory and geometric topology. These techniques come from dimension theory, infinite-dimensional topology, continuum theory, the theory of (ultra)filters and descriptive set theory. In the coming period the researched will be concentrated on the following topics:
- The relation between compact homogeneous ANR's and topological manifolds.
- Function spaces and the topology of pointwise convergence.
- Color number of maps: relationship between dimension and index.
- Application of continuum theory to topological dynamics and compactification theory.
- The existence of special ultrafilters on countable sets that interact well with a given structure, e.g., the topology of the rationals.
- The structure of finitely additive measures on the integers.
- Mutual embeddability of special Boolean algebras.