# Betti number

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 $X$.

Title | Betti number |
---|---|

Canonical name | BettiNumber |

Date of creation | 2013-03-22 13:47:14 |

Last modified on | 2013-03-22 13:47:14 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 55N10 |

Related topic | homology^{} |

Related topic | HomologyTopologicalSpace |