Topology understands objects as if they were made of rubber and could transform. In fact, the properties of objects remain unchanged although its shape is alterable. If we think of a circle, is a geometrical figure but if you can manipulate it becomes another figure: a triangle or an ellipse. This particular example gives a guideline of a basic principle of the topology: the equivalence between the figures. Two figures are equivalent if one is convertible into another.
If we start from the idea that the surfaces of objects are modifiable (think of a sheet of paper that can be cut or fold), is easy to see that the concrete applications of topology are immense. Computer programs are used to edit images. In the optics of lenses structure is altered. Industry items are subject to variations in its forms.
These examples demonstrate the versatility of the topology.
From a theoretical point of view the topology is related to other operations of Mathematics (differential equations, statistics...). However, what is striking in the topology is its ability to solve practical problems: analyze the best routing for the distribution of goods, or how to modify an object without breaking it. At the same time, topology has provided a model and a basic structure very useful for biology, specifically for the explanation of DNA. The genetic material is distributed in two complementary strings, the double helix, winding through the same axle. And the curvature of the shaft is a topological form.
In conclusion, the topology is based on a series of theoretical and abstract principles and from these it is possible to apply them to a multitude of areas of knowledge. Indeed, despite the complexity of this branch of mathematics, according to psychology the children handle intuitively the principles of topology in their games and the manipulation of objects.
Article contributed by the team of collaborators.