**Topology** is a modern branch of mathematics which formalizes the processes of **stretching** and **deforming** without tearing, as well as of *cutting and pasting* to construct new spaces, new geometries. It is called the *treatise of position* and *continuous phenomena*. Popularizations of **topology** have described it as *rubber-sheet-geometry*, where the concept of *position* is key, instead of *distance*.

The term **topology** refers also to the configuration of objects (and gives information) which helps to determine better stages for functioning.
In informatics it is common to hear about the **topology** of a network of computers. Modern abstract work with sophisticated application to physics, are -for example- knot theory and 3-manifolds.

In the language of category theory, **topology** studies the category consisting of *objects* called topological spaces and the *morphisms*
which correspond to continuous mappings and homeomorphism between the objects.

Subjects of study split **topology** into the non-disjoint sub-topics

## History

Topology has one of its roots in the need of generalizing the main concepts of real analysis: metrics and distances in Euclidean space $ \mathbb{R}^n $, open and closed sets, accumulation points or limit points, compact set and connected sets, $ \liminf $ and $ \limsup $. Some of this proto-primary concepts are also present in complex variables and functional analysis which are in the core of modern applied math.

Also in order to solve problems concerning combination, topology is like anything.