# retract

Let $X$ be a topological space^{} and $Y$ a subspace^{} of $X$. If there exists a continuous map^{} $r:X\to Y$ such that $r(y)=y$ for all $y\in Y$, then we say $Y$ is a *retract* of $X$ and $r$ is a *retraction*.

Title | retract |
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Canonical name | Retract |

Date of creation | 2013-03-22 12:16:06 |

Last modified on | 2013-03-22 12:16:06 |

Owner | rspuzio (6075) |

Last modified by | rspuzio (6075) |

Numerical id | 6 |

Author | rspuzio (6075) |

Entry type | Definition |

Classification | msc 54C15 |

Related topic | DeformationRetraction |

Related topic | PeriodOfMapping |

Defines | retraction |