KindiakMath

Topology

Here are my write-ups on the theory of topology and some non-trivial exercises therein. Any meaningful study across topics in mathematics will inevitably require the tools and techniques in topology. Enjoy!

Theory

Baby Topology

  1. Generalising Continuity
  2. Multivariable Topology
  3. Converging Confusions
  4. The Opposite of Open
  5. Topological Boundedness
  6. Connecting Theorems

Metric Matters

  1. Complete Metrics
  2. Banach’s Key Points
  3. The Sum of Powers
  4. Completing the Compact Space
  5. Compact Products
  6. The Hunt for Metrizability
  7. Hausdorff’s Relatives
  8. Urysohn’s Lemma
  9. Revisiting Metrizability

Revisiting Compactness

  1. Compactifying the Reals
  2. Baby Compactification
  3. Compact Products on Steroids
  4. Compactification on Steroids
  5. Arzelà-Ascoli Theorem

Applied Topology

  1. The Power of Compact Manifolds
  2. A Taste of Algebraic Topology
  3. Computing Topological Groups
  4. Surprising Theorems with Short Proofs
  5. Topological Vector Spaces

Exercises

Baby Topology

  1. A Taste of Topology
  2. Topological Continuity
  3. The Metric Topology
  4. Hausdorff Bookkeeping

Metric Matters

  1. Baire Category Theorem
  2. Several Metrization Lemmas
  3. Tietze Extension Theorem

Revisiting Compactness

  1. Arzelà-Ascoli Applied