Example image of eyePlorer eyePlorer map for 'Hopf–Rinow theorem': Complete metric space Geodesic Mathematics Riemannian manifold Heinz Hopf Bounded set Closed Compact space Exponential map Subset Tangent space Extrema Closed set Intrinsic metric Locally compact space List of theorems Sobolev inequality Finsler manifold Geodesics as Hamiltonian flows Rindler coordinates Shape of the Universe Differential geometry of surfaces