# restriction of a function

## Definition

Let $f:X\to Y$ be a function from a set $X$ to a set $Y$.
If $A$ is a subset of $X$,
then the *restriction ^{} of $f$ to $A$* is the function

${f|}_{A}:A$ | $\to $ | $Y$ | ||

$x$ | $\mapsto $ | $f(x).$ |

Some authors write $f\upharpoonright A$ instead of ${f|}_{A}$.

## Properties

If $A\subseteq X$, and $B\subseteq Y$, then

${({f|}_{A})}^{-1}(B)$ | $=$ | $A\cap {f}^{-1}(B).$ |

Title | restriction of a function |
---|---|

Canonical name | RestrictionOfAFunction |

Date of creation | 2013-03-22 13:43:05 |

Last modified on | 2013-03-22 13:43:05 |

Owner | yark (2760) |

Last modified by | yark (2760) |

Numerical id | 14 |

Author | yark (2760) |

Entry type | Definition |

Classification | msc 03E20 |

Synonym | restriction |

Related topic | Pullback2 |

Related topic | ExtensionOfAFunction |