List of general topology topics

This is a list of general topology topics.

Basic concepts

• Topological space
• Topological property
• Open set, closed set
• Clopen set
• Closure
• Boundary
• Interior
• Density
• G-delta set, F-sigma set
• Closeness
• Neighborhood
• Continuity (topology)
• Homeomorphism
• Local homeomorphism
• Open and closed maps
• Embedding
• Germ
• Basis
• Subbasis
• Open cover
• Locally finite space
• Covering space
• Atlas

Limits

• Limit point
• Net
• Filter
• Ultrafilter

Topological properties

• Baire category theorem
• Nowhere dense
• Baire space
• Banach–Mazur game
• Meagre set
• Comeagre set

Compactness and countability

• Compact space
• Relatively compact subspace
• Heine–Borel theorem
• Tychonoff's theorem
• Finite intersection property
• Compactification
• Measure of non-compactness
• Paracompact space
• Locally compact space
• Compactly generated space
• Axiom of countability
• Sequential space
• First-countable space
• Second-countable space
• Separable space
• Lindelöf space
• Sigma-compact space

Connectedness

• Connected space
• Simply connected space
• Path connected space

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

Topological constructions

• Direct sum and the dual construction product
• Subspace and the dual construction quotient
• Topological tensor product

Examples

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

Uniform spaces

• Uniform continuity
• Lipschitz continuity
• Uniform isomorphism
• Uniform property
• Uniformly connected space

Metric spaces

• Metric topology
• Manhattan distance
• Ultrametric space
• P-adic numbers, p-adic analysis
• Open ball
• Bounded subset
• Pointwise convergence
• Metrization theorems
• Complete space
• Cauchy sequence
• Banach fixed-point theorem
• Polish space
• Hausdorff distance
• Intrinsic metric
• Category of metric spaces

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

Descriptive set theory

• Polish Space
• Cantor space

Dimension theory

• Inductive dimension
• Lebesgue covering dimension
• Lebesgue's number lemma

Combinatorial topology

• Polytope
• Simplex
• Simplicial complex
• CW complex
• Manifold
• Triangulation
• Barycentric subdivision
• Sperner's lemma
• Simplicial approximation theorem
• Nerve of an open covering

Foundations of algebraic topology

• Simply connected
• Semi-locally simply connected
• Path (topology)
• Homotopy
• Homotopy lifting property
• Pointed space
• Wedge sum
• Smash product
• Cone (topology)
• Adjunction space

Topology and algebra

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

See also

• Topology glossary
• List of topologies
• List of topology topics
• List of geometric topology topics
• List of algebraic topology topics
• Publications in topology