# List of topology topics

In mathematics, **topology** (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.

A topological space is a set endowed with a structure, called a *topology*, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; connectedness, which allows distinguishing a circle from two non-intersecting circles.

The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the *geometria situs* and *analysis situs*. Leonhard Euler's Seven Bridges of Königsberg problem and polyhedron formula are arguably the field's first theorems. The term *topology* was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed.

This is a list of topology topics, by Wikipedia page. See also:

- Topology glossary
- List of topologies
- List of general topology topics
- List of geometric topology topics
- List of algebraic topology topics
- List of topological invariants (topological properties)
- Publications in topology

## Topology and physics[edit]

- Quantum topology
- Topological defect
- Topological entropy in physics
- Topological order
- Topological quantum field theory
- Topological quantum number
- Topological string theory
- Topology of the universe

## Topology and dynamical systems[edit]

- Milnor–Thurston kneading theory
- Topological conjugacy
- Topological dynamics
- Topological entropy
- Topological mixing

## Topology and computing[edit]

- Computational topology
- Digital topology
- Network topology
- Topological computing
- Topological Quantum Computing
- Topological quantum computer

## Miscellaneous[edit]

- Combinatorial topology
- Counterexamples in Topology
- Differential topology
- Geometric topology
- Geospatial topology
- Grothendieck topology
- Link (knot theory)
- Listing number
- Mereotopology
- Noncommutative topology
- Pointless topology
- Set-theoretic topology
- Topological combinatorics
- Topological data analysis
- Topological degree theory
- Topological game
- Topological graph theory
- Topological K-theory
- Topological modular forms
- Topological skeleton
- Topology optimization
- Water, gas, and electricity