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