Given a function f:XY, a fibre is an inverse image of an element of Y. That is given yY, f-1({y})={xXf(x)=y} is a fibre.

Example: Define f:2 by f(x,y)=x2+y2. Then the fibres of f consist of concentric circles about the origin, the origin itself, and empty setsMathworldPlanetmath depending on whether we look at the inverse image of a positive number, zero, or a negative number respectively.

Example: Suppose M is a manifold, and π:TMM is the canonical projection from the tangent bundle TM to M. Then fibres of π are the tangent spaces Tx(M) for xM.

Title fibre
Canonical name Fibre
Date of creation 2013-03-22 12:55:23
Last modified on 2013-03-22 12:55:23
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Definition
Classification msc 03E20
Synonym fiber
Related topic LevelSet