course material
Math:5701
Course
A. TOPOLOGY 1-Separation axioms: Hausdorff, regular and normal spaces
2- Quotient spaces (Munkres,
a) Quotient map, quotient topology b) Quotient topology by equivalence relation; various examples, such as, Torus, M¨obius strip, Klein bottle, n-dimensional real projective spaces RPn 3- Connectedness (Munkres, Chapter 3) a) Connected spaces b) Path connected spaces c) Components, path components, relation between path components and components d) Locally connected spaces, locally path connected spaces 4- Locally compact spaces, and the one-point compactification 5- Complete metric spaces and examples B. DIFFERENTIABLE MANIFOLDS Definition of smooth manifolds with related basic notions and various examples