# pointed topological space

Definition Suppose $X$ is a non-empty topological space^{} and ${x}_{0}$ is an
element of $X$. Then the pair $(X,{x}_{0})$ is called a
*pointed topological space ^{}*, or a

*based topological space*.

The idea with pointed topological spaces is simply that one fixes a base point
in the space. This is necessary, for instance, when defining the fundamental
group^{} of a topological space.

Title | pointed topological space |
---|---|

Canonical name | PointedTopologicalSpace |

Date of creation | 2013-03-22 14:01:15 |

Last modified on | 2013-03-22 14:01:15 |

Owner | bwebste (988) |

Last modified by | bwebste (988) |

Numerical id | 7 |

Author | bwebste (988) |

Entry type | Definition |

Classification | msc 54-00 |

Classification | msc 54E99 |

Synonym | based topological space |

Related topic | CategoryOfPointedTopologicalSpaces |

Related topic | PolishGSpace |

Related topic | OmegaSpectrum |