Continuity Without Epsilon-Delta
Central Question
Why is continuity expressed through inverse images of open sets?
Why This Matters
Recasting continuity makes it independent of coordinates and distances while retaining its familiar meaning in metric spaces.
Learning Prompt
Reconstruct continuity topologically using inverse images of open sets. Explain deeply why inverse images appear. Derive the equivalence with epsilon-delta continuity for metric spaces and give examples where the topological definition is more natural.