Topology should be topology, a discipline developed from geometry and set theory, which can be understood as a theoretical science to study concepts such as space, dimension and transformation. Simply put, topology is a branch of mathematics that studies continuity and connectivity.

Its definition is: Topology is the study of certain properties of geometric figures or spaces that can remain unchanged after continuous shape changes. Formally speaking, topology mainly studies the property that "topological space" remains unchanged under "continuous transformation".

Topology only considers the positional relationship between objects without considering their shapes and sizes when studying the changes of geometric shapes of objects.

Topology does not discuss the concept of congruence between two graphs, but the concept of topological equivalence. For example, circles, squares and triangles have different shapes and sizes, but they are all equivalent graphs under topological transformation; Football and rugby are also comparable. Because from a topological point of view, their topological structures are exactly the same.

The surface of swimming ring and the surface of football have different topological properties, for example, there is a "hole" in the middle of swimming ring. In topology, the space represented by football is called sphere, the space represented by swimming ring is called torus, and sphere and torus are "different" spaces.

Well-known topological problems include: one stroke problem, four-color map problem, Mobius surface, Klein bottle and so on.

Topology has been applied to physics, chemistry, biology, linguistics and even economics.

Klein bottle