The List of general topology topics reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

List of general topology topics

This is a list of general topology topics, by Wikipedia page. See also topology glossary, List of examples in general topology.

Table of contents

1 Metric spaces 2 Topological spaces: basic terms 3 Topological spaces: examples 4 Topology and order theory 5 Compact spaces 6 Separation axioms 7 Countability 8 Descriptive set theory 9 Dimension theory 10 Topological algebra 11 Combinatorial topology 12 Foundations of algebraic topology

Metric spaces

• Metric topology
• 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
• Category of metric spaces

Topological spaces: basic terms

• Open set
• Closed set
• Closure (mathematics)
• Clopen set
• Dense (topology)
• Limit point
• Separable
• Boundary, boundary (topology)
• Base (topology)
• Subbase
• G-delta set, F-sigma set
• Germ (mathematics)
• Atlas (topology)

Topological spaces: examples

• Discrete space
  • Locally constant function
  • Connected space
• Trivial topology
• Cofinite topology
• Finer topology
• Product topology
  • Restricted product
• Quotient space
• Unit interval
• Continuum (mathematics)
• Extended real number line
• Long line (topology)
• Sierpinski space
• Cantor set, Cantor space
• Space-filling curve
• Topologist's sine curve
• Uniform norm
• Weak topology
• Strong topology
• Hilbert cube
• Lower limit topology
• Real tree
• Zariski topology
• Kuratowski closure axioms
• Unicoherent

Topology and order theory

• Stone duality
  • Stone's representation theorem for Boolean algebras
• Specialization (pre)order
• Sober space
• Spectral space
• Alexandrov topology
• Upper topology
• Scott topology
  • Scott continuity
• Lawson topology

Compact spaces

• Heine-Borel theorem
• Finite intersection property
• Compactification
• Relatively compact subspace
• 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
• Sigma-compactness
• Net (mathematics)
• Ultrafilter

Descriptive set theory

Dimension theory

See also main article dimension

• Lebesgue covering dimension

Topological algebra

• Topological group
• Topological abelian group
• Topological ring
• Topological vector space
• Properly discontinuous
• Sheaf space

Combinatorial topology

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

Foundations of algebraic topology

• Simply connected
• Semi-locally simply connected
• Homotopy lifting property
• Barycentric subdivision
• Simplicial approximation theorem
• Nerve of an open covering
• Local homeomorphism
• Sheaf space
• Open map

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