1. Topology provides new research methods and tools for other disciplines. For example, the fixed point theory and homoethics in topology have been widely used in differential equations, dynamic systems and other fields.
2. Topology provides a new perspective for geometry. The concept of space in topology is different from that in Euclidean geometry, and it is more abstract and generalized. This abstract method enables us to understand and study geometric problems at a higher level.
3. Topology provides a new theoretical basis for physics. For example, path integral in quantum field theory is based on topology. In addition, the research of new materials such as topological insulators and topological superconductors can not be separated from the support of topology.
4. Topology provides a new algorithm and model for computer science. For example,
In a word, topology is of great value in the research of advanced mathematics, which provides us with new research methods and tools to help us better understand and solve various complex mathematical problems.