List of general topology topics

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This is a list of general topology topics.

## Contents

* 1 Basic concepts
* 2 Limits
* 3 Topological properties
* 3.1 Compactness and countability
* 3.2 Connectedness
* 3.3 Separation axioms
* 4 Topological constructions
* 5 Examples
* 6 Uniform spaces
* 7 Metric spaces
* 8 Topology and order theory
* 9 Descriptive set theory
* 10 Dimension theory
* 11 Combinatorial topology
* 12 Foundations of algebraic topology
* 13 Topology and algebra
* 14 See also

## Basic concepts

* Topological space
* Topological property
* Open set, closed set
* Clopen set
* Closure
* Boundary
* 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

See also: List of examples in general topology

* 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

* v
* t
* e

Topology

Fields|

* General (point-set)
* Algebraic
* Combinatorial
* Continuum
* Differential
* Geometric
* low-dimensional
* Homology
* cohomology
* Set-theoretic

Key concepts|

* Open set / Closed set
* Continuity
* Space
* compact
* Hausdorff
* metric
* uniform
* Homotopy
* homotopy group
* fundamental group
* Simplicial complex
* CW complex
* Manifold

* Category
*   * Wikibook
* Wikiversity
* Topics
* general
* algebraic
* geometric
* Publications

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