collection / modern mathematics

Week 02 — Topology

Week 02 — Topology

Central Question

What remains of geometry when distance, angle, and coordinates are removed?

The Story

Strip away measurements, keep continuity, and then use deformation and algebra to ask what a space is really like.

\text{Metric}\rightarrow\text{Open Sets}\rightarrow\text{Topology}\rightarrow\text{Homeomorphism}\rightarrow\text{Topological Invariants}\rightarrow\text{Homotopy}\rightarrow\pi_1

Sessions

Connections Beyond This Week

Month overview · Exploration Map · Home

Related

Session 01 — From Metric Spaces to Topology Session 02 — Strange Topologies Session 03 — Continuity Without Epsilon-Delta Session 04 — Homeomorphism Session 05 — Connectedness Session 06 — Compactness Session 07 — Quotient Spaces Session 08 — Homotopy Session 09 — Fundamental Group Session 10 — Why the Circle Produces the Integers Session 11 — A Glimpse of Algebraic Topology Session 12 — Week 2 Synthesis Week 01 — Field Extensions and Galois Theory Week 03 — Geometry and Manifolds Month 01 — From Familiar Mathematics to Modern Mathematics Exploration Map Mathematics Exploration Library

Referenced by

Month 01 — From Familiar Mathematics to Modern Mathematics Week 01 — Field Extensions and Galois Theory Session 01 — From Metric Spaces to Topology Session 02 — Strange Topologies Session 03 — Continuity Without Epsilon-Delta Session 04 — Homeomorphism Session 05 — Connectedness Session 06 — Compactness Session 07 — Quotient Spaces Session 08 — Homotopy Session 09 — Fundamental Group Session 10 — Why the Circle Produces the Integers Session 11 — A Glimpse of Algebraic Topology Session 12 — Week 2 Synthesis Week 03 — Geometry and Manifolds Topology Mathematics Exploration Library