# extension of a function

Let $f:X\to Y$ be a function and $A$ and $B$ be sets such that $X\subseteq A$ and $Y\subseteq B$. An *extension ^{}* of $f$ to $A$ is a function $g:A\to B$ such that $f(x)=g(x)$ for all $x\in X$. Alternatively, $g$ is an extension of $f$ to $A$ if $f$ is the restriction

^{}of $g$ to $X$.

Typically, functions are not arbitrarily extended. Rather, it is usually insisted upon that extensions have certain properties. Examples include analytic continuations and meromorphic extensions.

Title | extension of a function |
---|---|

Canonical name | ExtensionOfAFunction |

Date of creation | 2013-03-22 17:51:00 |

Last modified on | 2013-03-22 17:51:00 |

Owner | Wkbj79 (1863) |

Last modified by | Wkbj79 (1863) |

Numerical id | 6 |

Author | Wkbj79 (1863) |

Entry type | Definition |

Classification | msc 03E20 |

Related topic | RestrictionOfAFunction |

Defines | extension |