List of general topology topics

Metric spaces

• Manhattan distance
• Ultrametric space
  • P-adic numbers, p-adic analysis
• Open ball
• Uniform continuity
  • Lipschitz continuity
  • Uniform space
• Bounded
• Pointwise convergence
• Metrization theorems
• Complete space
  • Cauchy sequence
  • Banach fixed point theorem
• Baire category theorem
  • Nowhere dense
  • Baire space
  • Banach-Mazur game
  • Co-meagre
• Polish space
• Hausdorff distance
• Intrinsic metric

Topological spaces: basic terms

• Open set
• Closed set
• Closure (mathematics)
• Clopen set
• Dense (topology)
• Limit point
• Separable
• Boundary
• G-delta set
• Germ (mathematics)
• Atlas (topology)

Topological spaces: examples

• Discrete space
  • Locally constant function
  • Connected space
• Trivial topology
• Finer topology
• Product topology
  • Restricted product
• 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
• Lower limit topology
• Real tree
• Zariski topology
• Kuratowski closure axioms
• Unicoherent

Compact spaces

• Finite intersection property
• Compactification
• Tychonoff's theorem
• Locally compact space
• Measure of non-compactness

Separation axioms

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

Countability

• Axiom of countability
• Second countable
• Lindelöf space
• Net (mathematics)
• Ultrafilter

Descriptive set theory

Topological algebra

• Topological group
• Topological ring
• Topological vector space
• Properly discontinuous
• Stone's duality
• Sheaf space

Combinatorial topology

• Polytope
• Simplex
• Simplicial complex
• CW complex
• Manifold
• Triangulation
• Sperner's lemma

Referenced By