Programme leaders: J. van Mill, J.M. Aarts
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
research 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.
- Measures on compact L-spaces (the so-called Kunen spaces).
- Zerodimensional and pseudocompact topological groups.
- The relationship between dimension theory and the preservation of fixed
points under extensions of maps (Ljusternik-Schnirelman).
- Application of continuum theory to topological dynamics and compactification
theory.