topology - définition. Qu'est-ce que topology
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Qu'est-ce (qui) est topology - définition

BRANCH OF MATHEMATICS
TopOlogy; Topologically; Topological; Topologist; Topological analysis; Topologies; Topology (Mathematics); History of topology; Topology (mathematics); Applications of topology
  • A continuous transformation can turn a coffee mug into a donut.<br>Ceramic model by Keenan Crane and [[Henry Segerman]].
  • figure-eight knot]]. The figure-eight knot is a [[prime knot]] and has an [[Alexander–Briggs notation]] of 4<sub>1</sub>.

topology         
1. <mathematics> The branch of mathematics dealing with continuous transformations. 2. <networking> Which hosts are directly connected to which other hosts in a network. Network layer processes need to consider the current network topology to be able to route packets to their final destination reliably and efficiently. (2001-03-29)
topology         
[t?'p?l?d?i]
¦ noun (plural topologies)
1. Mathematics the study of geometrical properties and spatial relations which remain unaffected by smooth changes in shape or size of figures.
2. the way in which constituent parts are interrelated or arranged.
Derivatives
topological adjective
topologically adverb
topologist noun
Origin
C19: via Ger. from Gk topos 'place' + -logy.
Topology         
·noun The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

Wikipédia

Topology

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; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.

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.

Exemples du corpus de texte pour topology
1. It concerns the geometry of multidimensional spaces and is key to the field of topology.
2. The conjecture is a central question in topology, the study of the geometrical properties of objects that do not change when the they are stretched, distorted or shrunk.
3. The celebrated problem concerns the geometry of multidimensional spaces and is key to the field of topology, the branch of maths that deals with shapes.
4. The prospects for chaos over the next few days mounted yesterday with a group calling itself the Deconstructionist Institute for Surreal Topology issuing leaflets advising people how to blockade the Gleneagles hotel, where G8 leaders will be staying.
5. Senior police officers involved in planning future anti–terrorist strategy are struggling to draw up a new topology of what makes a young British Muslim want to become a martyr for the jihad.