Borel hierarchy

The Borel hierarchy is a way mathematicians classify different types of sets within a topological space, like the real numbers, based on how they can be constructed through operations like countable unions and intersections starting from simple open sets. It organizes sets into levels, called Borel classes, each built from the previous ones, creating a hierarchy that shows increasing complexity. This structure helps mathematicians understand the properties and relationships of sets in analysis and topology, especially in areas related to measure and probability, by providing a systematic framework for their classification.