Complex and symplectic geometry
Manifolds with complex, almost complex, symplectic or contact structures, Riemann surfaces, and integrable Hamiltonian systems.
- Darboux's theorem
- Identity and open mapping theorems for holomorphic maps
- Liouville–Arnold theorem
- Newlander–Nirenberg theorem
- Weinstein conjecture
TheoremRadó's theorem#●ready to prove
MathlibExt.Geometry.RadoTheoremWanted.Geometry.rado_riemannSurface
Every connected Riemann surface is second countable: if \(X\) is a connected Hausdorff topological space with an atlas of charts to \(\mathbb{C}\) whose transition maps are of class \(C^1\) over \(\mathbb{C}\) (that is, holomorphic), then the topology of \(X\) is second countable.
public theorem_wanted rado_riemannSurface {X : Type*} [TopologicalSpace X] [T2Space X] [ConnectedSpace X]
[ChartedSpace ℂ X] [IsManifold (modelWithCornersSelf ℂ ℂ) 1 X] :
SecondCountableTopology XSources
Sources
- John Hamal Hubbard, Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1, §1.3. Problem
rado_riemannSurfaceof the lean-eval benchmark.
Loading dependency explorer…
The dependency explorer needs JavaScript and its graph data.