General (point-set) topology

By the end you’ll be able to

• Check whether a collection of subsets is a topology, and compare topologies such as discrete, indiscrete, cofinite and the usual topology
• Determine whether functions between topological spaces are continuous and identify homeomorphisms and topological invariants
• Decide compactness, connectedness, path-connectedness and the Hausdorff property, including in non-standard topologies