Betti numberBettiNumber2003-07-23 15:39:282006-08-15 20:33:26Definitionhomology% this is the default PlanetMath preamble. as your knowledge
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Let $X$ denote a topological space, and let $H_k(X,\Z)$ denote the $k$-th homology group of $X$. If $H_k(X,\Z)$ is finitely generated, then its rank is called the $k$-th \emph{Betti number} of $X$.