Topology is a branch of mathematics, which mainly studies the nature and structure of space. In recent years, the research status of topology has the following characteristics:

1. In-depth theoretical research: The basic theories of topology have been deepened continuously, including homotopy theory, homology theory theory and K theory, and important progress has been made. At the same time, the interdisciplinary research between topology and other mathematical fields is also strengthening, such as topology and algebra, geometry, analysis and other fields.

2. Wide application: The theory and method of topology have been widely used in physics, chemistry, biology, computer science and other fields. For example, in quantum field theory, the study of topological state of matter has become an important research direction. In biology, topological methods are used to study the structure and function of protein.

3. Update of technical means: With the development of computer technology, topologists have been able to use computer simulation to study complex topological structures. This not only greatly improves the efficiency of research, but also makes some problems that were difficult to solve before possible.

4. Education popularization: With the continuous development of topology, its application in education is more and more extensive. Many universities have offered courses in topology and trained a large number of topology talents.

Generally speaking, the research status of topology is active and the prospect is broad. However, topology is still a challenging field, and there are still many unsolved problems waiting for us to explore and solve.