# List of general topology topics

This is a **list of general topology topics**, by Wikipedia page.

## Basic concepts

- Topological space
- Topological property
- Open set, closed set
- Continuity (topology)
- Base (topology), subbase
- Open cover
- Covering space
- Atlas (topology)

## Limits

## Topological properties

### 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

### Separation axioms

- 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

See also: List of examples in general topology

- Discrete space
- Trivial topology
- Cofinite topology
- Finer topology
- Product topology
- 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
- 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

## Descriptive set theory

## Dimension theory

*See also main article dimension*

## 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 topology topics
- List of geometric topology topics
- List of algebraic topology topics
- Publications in topology

This article is issued from Wikipedia - version of the 10/11/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.