Betti number

noun1

1. •
   Any of a sequence of numbers, denoted bₙ, which characterise a given topological space K by giving, for each dimension, the number of holes in K of said dimension; (formally) the rank of the nth homology group, Hₙ, of K.

   • Poincaré proved that Betti numbers are invariants and used them to extend Euler's polyhedral formula to higher dimensional spaces.