Betti Number
In algebraic topology, a mathematical discipline, the Betti numbers can be used to distinguish topological spaces. Intuitively, the first Betti number of a space counts the maximum number of cuts that can be made without dividing the space into two pieces.
Each Betti number is a natural number or +∞. For the most reasonable finite-dimensional spaces (such as compact manifolds, finite simplicial complexes or CW complexes), the sequence of Betti numbers is 0 from some points onwards (Betti numbers vanish above the dimension of a space), and they are all finite.
The term "Betti numbers" was coined by Henri Poincaré after Enrico Betti.
Read more about Betti Number: Informal Definition, Definition, Example: The First Betti Number in Graph Theory, Properties, Examples, Relationship With Dimensions of Spaces of Differential Forms
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—John Major (b. 1943)