# countably compact

A topological space^{} $X$ is said to be *countably compact* if every countable^{} open cover has a finite subcover.

Countable compactness is equivalent^{} to limit point compactness if $A$ is ${T}_{1}$ spaces, and is equivalent to compactness (http://planetmath.org/Compact^{}) if $X$ is a metric space.

Title | countably compact |
---|---|

Canonical name | CountablyCompact |

Date of creation | 2013-03-22 12:06:43 |

Last modified on | 2013-03-22 12:06:43 |

Owner | Evandar (27) |

Last modified by | Evandar (27) |

Numerical id | 8 |

Author | Evandar (27) |

Entry type | Definition |

Classification | msc 54D20 |

Synonym | countable compactness |

Related topic | Compact |

Related topic | Lindelof |

Related topic | LimitPointCompact |