What is topology?

Topology is a branch of mathematics that deals with the study of surfaces or abstract spaces where the measurable amount is not important. Given this unique approach to mathematics, topology is sometimes referred to as the geometry of rubber leaves, because the shapes considered exist on infinitely distributed rubber leaves. In typical geometry, the basis for all calculations are basic shapes, such as a circle, square and rectangle, but in topology is the basis of continuity and position of points in relation to each other. The topological map can have points that together to form a geometric shape such as a triangle. This collection of points is considered a space that remains unchanged; No matter how twisted or outstretched, it would remain unchanged as a rubber leaf point no matter what form it was. This kind of conceptual framework for mathematics is often used in areas where deformates in large or small scale are ion, such as gravitational wells in space,Analysis of particle physics at sub-atomic level and in a study of biological structures such as changing proteins.

4 such shapes that share the same features are referred to as homeomorphic. An example of two topological shapes that are not homeomorphic or cannot be changed to resemble each other, balls and torus or donut shape.

The discovery of basic spatial properties of defined spaces is the primary goal in topology. The topological map of the basic level set is referred to as a set of Euclidean premises. The gaps are categorized according to their number of dimensions, where the line is in one dimension and a plane of the ancestor in two. The space experienced by human beings is referred to as a three -dimensional Euclidean space. More complex sets of spaces are called pipes that appear different from the local level than in a large scale.

pipe sets and node theory are trying to explain the surfacesIn many dimensions beyond what is perceptible at a literal human level, and the premises are associated with algebraic invariants to classify them. This process of homotopia theory or the relationship between identical topological spaces was launched by Henri Poincar & Eacute, a French mathematician who lived from 1854 to 1912. Mathematics have shown the work of Poincar & Eacute in dimensions, but three.