Analysis of carrying capacity of higher education based on topological number theory in the context of ecological theory of education

This paper focuses on analyzing the educational carrying capacity of colleges and universities by using topological number theory and the educational carrying capacity development index. The scale range of the educational carrying capacity of colleges and universities can be determined by identifying relevant definitions of topological space and some topological invariants. Using the relevant definitions of topological space to divide the college education-bearing intervals of different regions and combining the human development index and imbalance coefficient processing, we construct the formula of the balanced and sufficient development index of college education-bearing capacity, which is used to analyze the education bearing capacity of colleges and universities. Analyze different states of college education carrying capacity based on the college education carrying capacity bearing structure. Examine the educational carrying capacity of colleges and universities by examining their educational resource allocation with the help of human and financial resources. The results show that the teacher-student ratio of the urban function expansion area is 0.052, which is the smallest teacher-student ratio among all the districts, indicating that although the district is rich in teachers’ resources, the balanced and sufficient development index of the educational carrying capacity of colleges and universities in District A and District D is high, and the top two rankings have been maintained for a long period in the process of development, and the index of the balanced and sufficient development of education in District A will be 60 in 2021, which is in the area of the development of higher value of the educational carrying capacity.