#Math101 Session 29

Time：Sep. 25, 2025, 15:00-17:00

Location：E104 Hai Tian Building, Chang'an Campus

Speaker：Mr. Yang, Dongyu (Class of 2024)

Title：Relation, mapping, and indexed family of sets

Abstract：This talk first introduces the concept of an equivalence relation, a binary relation that is reflexive, symmetric, and transitive. We then explore the notion of general mappings, highlighting their fundamental properties. Next, we discuss indexed families of sets, where each set is associated with a unique element from an index set. Unlike a simple collection of sets, an indexed family can be viewed as a mapping from the index set to the collection of sets, allowing for repeated sets and more flexible structures. Finally, we examine how operations such as union and intersection on indexed families help generate more complex algebraic structures, including sigma-algebras.