Topological space
In topology and related branches of mathematics, a topological space may be defined as a set of points, along with a set of neighborhoods for each point, satisfying a set of axioms relating points and neighborhoods.
Description
The definition of a topological space relies only upon set theory and is the most general notion of a mathematical space that allows for the definition of concepts such as continuity, connectedness, and convergence.
Other spaces, such as manifolds and metric spaces, are specializations of topological spaces with extra structures or constraints.
Being so general, topological spaces are a central unifying notion and appear in virtually every branch of modern mathematics.
The branch of mathematics that studies topological spaces in their own right is called point-set topology or general topology.
See also
- Accessible/Fréchet space (T1)
- Complete Heyting algebra – The system of all open sets of a given topological space ordered by inclusion is a complete Heyting algebra.
- Completely Hausdorff space and Urysohn space (T2½)
- Completely normal Hausdorff space (T5)
- General topology
- Hausdorff space (T2)
- Kolmogorov space (T0)
- Neighbourhood (mathematics)
- Normal Hausdorff space (T4)
- Perfectly normal Hausdorff space (T6)
- Point (geometry)
- Quasitopological space
- Regular space and regular Hausdorff space (T3)
- Tychonoff space and completely regular space (T3½)
- Space (mathematics)
External links
- Topological space @ Wikipedia.org
