- Definition, characterisations
- Constructions
- Bases
- Continuity continuity and constructions
- Separation separation and constructions
- Countability, density
- Compact spaces proper and continuous maps are closed, alexandroff and stone-cech compactifications, tychonoff, compactness and constructions, paracompactness and partition of unity
- Filters
- Connected spaces connectedness and constructions
- Miscellaneous spaces
- Nets
- Order topology and semicontinuity
- Uniform spaces uniform (equi-)continuity, uniform completion, image of complete spaces in complete spaces, closed subspace of complete space is complete, Tietze–Urysohn for normal spaces and equicontinuity
- Metric spaces pseudometrics (alexandroff in metric setting? or uniform?), metrizability theorem
- The compact-open topology
- Homotopy things which are invariant under homotopy
- Covering spaces proper local homeomorphisms are precisely finite covering maps
- Fiber bundles and fibrations
- CW complexes
- Simplicial complexes
- Pointed spaces and support
Sources
- Bourbaki, General Topology
- Grothendieck TVS
- Hatcher Algebraic Topology
- Lamotke Semisimpliziale algebraische Topologie
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