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Betti number (Definition)

Let $ X$ denote a topological space, and let $ H_k(X,\mathbb{Z})$ denote the $ k$-th homology group of $ X$. If $ H_k(X,\mathbb{Z})$ is finitely generated, then its rank is called the $ k$-th Betti number of $ X$.



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See Also: homology, homology

Keywords:  homology
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Cross-references: finitely generated, homology group, topological space
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This is version 3 of Betti number, born on 2003-07-23, modified 2006-08-15.
Object id is 4498, canonical name is BettiNumber.
Accessed 4149 times total.

Classification:
AMS MSC: 55N10 (Algebraic topology :: Homology and cohomology theories :: Singular theory)
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