Math 5701

Geometry and Topology
Connected spaces, Path connected spaces, Connected components, Locally
connected spaces, Quotient spaces, The separation axioms (Hausdorff,
Regular, Normal). Differentiable manifolds, Submanifolds of R^n
and Classical
Lie groups, Tangent spaces, Differentiable mappings between manifolds,
Inverse and Implicit function theorems on manifolds.