Topology

Topology topology is a modern area of ​​geometry. Topological geometers are not qualitative geometry because they take into account the features that can not be changed by stretching, twisting or shrinking the object, not the traditional features (angle, length, etc.) of the object. Even after the change, all the points in the connected object will remain connected, and all the points separated by the holes will remain isolated. In the topology, we also try to interpret objects that do not exist in three dimensions using mathematical expressions. This is because it is almost impossible to imagine such an object in the reference frame.

The topology can be roughly divided into three branches: a point set topology, a combined topology, and an algebraic topology. Point set topology (often also simply referred to as general topology) treats the graph as a set of points with attributes such as open or closed, compact, connection etc. Compared to point-set topology, the composite topology treats the graph as a combination (complex) of simple graphics (simple shapes) connected together in a conventional manner. Algebraic methods are widely used in algebraic topology, especially group theory. There is also a topological part where these branches overlap

Topological thinking exists in almost all fields of today's mathematics. The topology itself consists of several different branches with relatively few common points such as point set topology, algebraic topology, differential topology. It tracks the occurrence of topology concepts in various situations. Perhaps the first work worth considering as a topology start is by Euler. In 1736 Euler published a paper on Konigsberg Bridge problem solving method. This translates English into a solution to location geometry problems. The title itself shows that Euler knows that it deals with various types of geometry unrelated to distance.

Poincaré has created an algebraic (coupled) topology theory. This is also called "the father of the topology" (also known as the title of Euler and Brouwer). He has also done excellent work in other areas of mathematics; he is one of the most creative mathematicians in history, the largest mathematician in the style of constructivism ("intuitionism"). He has published hundreds of articles on various topics and may have become the most abundant mathematician so far, but he died at the peak of his power. Poincaré was clumsy and unconscious; like Galois, he was almost denied access to the French university just because he was far from what he knew at the age of seventeen.