List of general topology topics

Table of contents

1 Metric spaces 2 Topological spaces: examples 3 Compact spaces 4 Separation axioms 5 Countability 6 Topological algebra 7 Combinatorial topology

Metric spaces

• Manhattan distance
• Ultrametric space
  • P-adic numbers, p-adic analysis
• Uniform continuity
  • Lipschitz continuity
  • Uniform space
• Pointwise convergence
• Metrization theorems
• Complete space
  • Cauchy sequence
  • Banach fixed point theorem
• Baire category theorem
  • Nowhere dense
  • Baire space

• Discrete space
  • Locally constant function
  • Connected space
• Product topology
• Quotient space
• Unit interval
• Extended real number line
• Long line
• Cantor set, Cantor space
• Space-filling curve
• Topologist's sine curve
• Uniform norm
• Hilbert cube
• Zariski topology
• Kuratowski closure axioms

• Compactification
• Tychonoff's theorem
• Locally compact space

• T0 space
• T1 space
• Hausdorff space
• Regular space
• Tychonoff space
• Normal space
• Urysohn's lemma
• Tietze extension theorem
• Paracompact
• Separated sets

• Second countable
• Lindelöf space
• Net (mathematics)
• Ultrafilter

• Topological group
• Topological ring
• Topological vector space

• Polytope
• Simplex
• Simplicial complex
• CW complex
• Manifold
• Triangulation