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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:

- 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