Borelhierarkin
The Borel hierarchy is a classification of subsets of a topological space, particularly the real numbers, based on their complexity. It was introduced by Émile Borel in the early 20th century. The hierarchy is defined recursively, with each level consisting of sets that can be constructed from sets of lower levels using countable unions, intersections, and complements.
The first level of the Borel hierarchy, denoted as Σ1, consists of open sets. The second level,
The Borel hierarchy is a proper hierarchy, meaning that each level contains sets that are not in
The Borel hierarchy has important applications in various areas of mathematics, including topology, measure theory, and