Adelic topology is a mathematical framework that combines various number systems, particularly in the study of algebraic numbers and algebraic geometry. It utilizes the concept of adeles, which are elements that incorporate information from both local and global fields, allowing mathematicians to analyze properties of numbers in a unified way. This topology is particularly useful in number theory, as it provides a way to study arithmetic geometry and the behavior of algebraic varieties over different fields. By considering the interactions between local and global properties, adelic topology helps in understanding complex structures in mathematics.