Homeomorphism

Central Question

What does it mean for two spaces to have the same topology?

Why This Matters

A notion of sameness needs both examples and obstructions. Homeomorphism sets the stage for distinguishing spaces through invariants rather than drawings.

Learning Prompt

Develop homeomorphism as the correct topological notion of sameness. Study examples such as $(0,1)\cong\mathbb R$ and an open disk $\cong\mathbb R^2$. Then make me reason about pairs of spaces using invariants rather than pictures alone.

Ideas

Examples

Questions

Connections

• When Different Constructions Give the Same Field
• Connectedness
• Compactness
• Fundamental Group
• Week overview

One Thing That Surprised Me

Further Rabbit Holes