Topology

Point set topology
  1. Topology I: limits, morphisms, the neighbourhood filter, open sets
  2. Topology II: Kuratowski closure topology, nets, neighbourhood basis, dense sets
  3. Topology III: example topologies, inherited topologies, distinguishability 
  4. Supplementary definitions: connectedness, clopen sets
  5. Supplementary definitions: compactness, compactification, hemicompactness
  6. Supplementary definitions: local stuff
  7. Supplementary definitions: levels of abstraction
  8. Supplementary definitions: paracompactness -- seeseesee
  9. Wrapping, unwrapping and simply connectedness
  10. Topology of Euclidean space, etc. -- seesee
  11. Metrisability -- seesee?
  12. Knot theory
Algebraic topology
  1. Paths, dimensions, Fundamental group, contractibility, homotopy, topological invariants, etc.
  2. Euler characteristic, etc.
Homology, Cohomology, Topology of derivatives and Stokes' theorem [1]

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