点集拓扑是现代数学中一门重要分支，它用公理化方法建立开集和邻域的概念，从而形成一个集合的拓扑结构，进而又讨论了在这一框架下空间的性质，如连续映射、连通性、可数性公理、分离公理、紧致性等问题。拓扑结构作为现代数学的三大机构之一，在许多数学分之中有广泛的应用。现在，点集拓扑已经发展成为内容丰富、方法系统、体系完备、应用广泛的分支。本课程是数学与应用数学专业的一门专业方向专业必修课。通过该课程的学习，可以使学生对点集拓扑的基本理论和方法有一定的了解，同时对其它数学分支如代数拓扑、泛函分析等的学习有一定的帮助。 Point set topology is an important branch of modern mathematics. It establishes the concepts of open sets and neighbourhoods based on the axiomatic method. And the continuity, connectivity, countability axioms, separation axioms, and compactness are discussed under the structure. Topology structure, which finds a lot of applications, is one of the three main structures: order structures, linear structures, and topology structures, in mathematics. The subject is the compulsory course for undergraduate students in the Department of Mathematics, Wuhan University of Technology. After studying the subject, students will be equipped with the ability to further study algebra topology, functional analysis and other branches of modern mathematics.