Topology The diffeomorphism group has two natural topologies: weak and strong . When the manifold is compact, these two topologies agree. The weak topology is always metrizable. When the manifold is not compact, the strong topology captures the behavior of functions "at infinity" and is not metrizable. It is, however, still Baire.
Topology The diffeomorphism group has two natural topologies weak and strong  When the manifold is compact these two topologies agree The weak topology is always metrizable When the manifold is not compact the strong topology captures the behavior of functions "at infinity" and is not metrizable It is however still Baire