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Topology

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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.

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