#Math101 Session 30

Time：Oct. 9, 2025, 14:00-16:00

Location：E104 Hai Tian Building, Chang'an Campus

Speaker：Miss Deng, Huixi (Class of 2024)

Title：Topological spaces and continuous mappings

Abstract：Modern mathematical analysis and geometry are deeply rooted in the concept of topological spaces, which provide a flexible yet rigorous framework for studying continuity, convergence, and connectedness beyond the limitations of metric spaces. In this talk, we first recollect basic concepts from mathematical analysis including continuity of a real-valued function, metric, neighborhood, etc. In light of the properties of the open sets in the Euclidean space, we introduce, following Bourbaki's abstract and axiomatic approach, the now-standard definition of a topological space in terms of open sets and set-theoretic operations. We will then examine how this abstraction facilitates the generalization of continuous mappings, allowing us to extend familiar notions from calculus to vastly more general settings.