1. set theory: set theory is the basis of mathematics, and many concepts in topology are based on set theory. For example, a topological space is a set, and its elements are called points. The concepts of open set and closed set are also based on set theory.
2. Real numbers and complex numbers: Topology often involves the operation of real numbers and complex numbers, so it is necessary to have a deep understanding of these basic concepts.
3. Calculus: Many concepts in topology, such as continuous mapping, compactness and connectivity, are related to calculus. Therefore, learning topology needs to master the basic knowledge of calculus.
4. Linear algebra: Linear algebra is a branch of mathematics that studies vector space and linear mapping. Many concepts in topology, such as embryo and regularity, are related to linear algebra.
5. Geometry: Topology is closely related to geometry, and many geometric concepts can be restated by topology. Therefore, learning topology requires a certain understanding of geometry.
6. Function theory: Function theory is a branch of mathematics that studies the properties of functions. Many concepts in topology, such as continuity and compactness, are related to function theory.
7. Analytics: Analytics is a branch of mathematics that studies infinite dimensional space. Many concepts in topology, such as compactness and completeness, are related to analysis.
Generally speaking, learning topology requires a solid mathematical foundation, including set theory, real and complex numbers, calculus, linear algebra, geometry, function theory and analysis.