Betti number

In algebraic topology, Betti numbers are a sequence of integers that provide important information about the topology of a topological space. They are used to classify spaces based on their connectivity properties and to understand their shape and structure. Specifically, the \(n\)-th Betti number, denoted \(b_n\), represents the rank of the \(n\)-th homology group \(H_n(X)\) of a topological space \(X\).