Descriptive Set Theory

Descriptive Set Theory is a branch of mathematical logic that studies certain collections of sets, particularly in relation to their complexity and structure. It focuses on sets of real numbers or points in space, classifying them into hierarchies based on properties like continuity and definability. By examining how these sets behave under various operations, Descriptive Set Theory reveals insights about limits, continuity, and functions. It connects areas of mathematics, such as topology and analysis, and has applications in fields like computer science, providing a framework for understanding infinitely complex structures and relationships.