Strange Topologies
Central Question
What can unusual choices of open sets teach us about convergence and continuity?
Why This Matters
Unfamiliar examples expose assumptions inherited from Euclidean intuition and clarify precisely what a topology does and does not record.
Learning Prompt
Explore discrete, indiscrete, cofinite and other interesting topologies. Investigate open and closed sets, convergence and continuity in them. Use these examples to clarify what information a topology actually encodes.