Topology
by Barbu Berceanu
Preliminary
version of the topics
for the Topology course:
Part 1: Basic notions
1) Topological spaces and continuous maps
2) Construction of new spaces
3) Countability and separation axioms
4) Connectedness
5) Compact spaces
Part 2: Main examples
6) Metric spaces
7) Complexes and manifolds
8) Topological groups
9) Function spaces
Part 3: Homotopy and fundamental
group
10) Homotopy, retracts, and deformations
11) Fundamental group and covering spaces
12) Computing fundamental group