# direct image

If $f:X\to Y$ is a continuous map^{} of topological spaces^{} and $\mathcal{F}$ is a sheaf on $X$, the direct image sheaf, ${f}_{*}\mathcal{F}$ on $Y$ is defined by

$({f}_{*}\mathcal{F})(V)=\mathcal{F}({f}^{-1}(V))$

for open sets $V\subset Y$, with the restriction^{} maps induced from those of $\mathcal{F}$.

Title | direct image |
---|---|

Canonical name | DirectImage1 |

Date of creation | 2013-03-22 12:03:10 |

Last modified on | 2013-03-22 12:03:10 |

Owner | nerdy2 (62) |

Last modified by | nerdy2 (62) |

Numerical id | 8 |

Author | nerdy2 (62) |

Entry type | Definition |

Classification | msc 54B40 |