Analytic Sets

Analytic sets are a class of complex objects in mathematical logic and set theory, specifically within the study of the real numbers and other spaces. They are formed through processes involving continuous functions applied to simpler sets, such as Borel sets, which are built from basic open or closed sets. Analytic sets include many "well-behaved" sets but can also be quite intricate, sometimes lacking certain regularity properties. They play a key role in descriptive set theory, helping mathematicians understand the structure and complexity of sets beyond classical categories like open or closed sets.