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 (topology)
 * Boundary (topology)
 * Dense (topology)
 * G-delta set, F-sigma set
 * closeness (mathematics)
 * neighbourhood (mathematics)
 * Continuity (topology)
 * Homeomorphism
 * Local homeomorphism
 * Open and closed maps
 * Germ (mathematics)
 * Base (topology), subbase
 * Open cover
 * Covering space
 * Atlas (topology)

Limits

 * Limit point
 * Net (topology)
 * Filter (topology)
 * 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

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
 * Finer topology
 * Product topology
 * Restricted product
 * Quotient space
 * Unit interval
 * Continuum (topology)
 * Extended real number line
 * Long line (topology)
 * Sierpinski space
 * Cantor set, Cantor space, Cantor cube
 * Space-filling curve
 * Topologist's sine curve
 * 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