#Math101 Session 31

Time：Oct. 16, 2025, 14:00-16:00

Location：E104 Hai Tian Building, Chang'an Campus

Speaker：Mr. Wang, Hongjian (Class of 2024)

Title：Subspace topology and topological basis

Abstract：Given a topological space and one subset, we in this talk first introduce the concept of subspace topology, establishing that it satisfies the axioms of a topology and characterizing it as the “coarsest” topology on the subset. We then discuss the topological basis, motivated by the idea that we do not want to describe a topology by explicitly specifying all of its open sets; we would rather take a much smaller collection of sets in the topology such that we could obtain all the open sets via taking unions of the above special ones. Some examples will be included.