Week 1: Compactness and separation axioms.
Week 2: Paracompactness and partition of unity.
Week 3: Various notions of Compactness in metric metric spaces, Ascoli’s theorem.
Week 4: Productive properties.
Week 5: Productive properties continued.
Week 6: Urysohn’s Metrization theorem.
Week 7: Compactifications 1-pt compactification, Stone-Cech Compactification.
Week 8: Totally disconnectedness.
Week 9: A brief introduction to dimension theory.
Week 10: Function spaces, Compact open topology, exponential correspondence.
Week 11: Stone-Weierstass Theorem.
Week 12: Ordinal Topology- a source for many counter examples.