ملحق المادة الدراسية
Math:5701
المقرر الدراسي
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