List of general topology topics
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Template:Short description This is a list of general topology topics.
Basic concepts
- Topological space
- Topological property
- Open set, closed set
- Continuity (topology)
- Basis
- Open cover
- Locally finite space
- Covering space
- Atlas
Limits
Compactness and countability
- Compact space
- 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
- T0 space
- T1 space
- 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
- Trivial topology
- Cofinite topology
- Cocountable topology
- Finer topology
- Product topology
- 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 continuity
- Lipschitz continuity
- Uniform isomorphism
- Uniform property
- Uniformly connected space
- Metric topology
- Manhattan distance
- Ultrametric space
- Open ball
- Bounded subset
- Pointwise convergence
- Metrization theorems
- Complete space
- Polish space
- Hausdorff distance
- Intrinsic metric
- Category of metric spaces
Topology and order theory
- Stone duality
- Specialization (pre)order
- Sober space
- Spectral space
- Alexandrov topology
- Upper topology
- Scott topology
- Lawson 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