Graph of a function: Difference between revisions

Revision as of 12:33, 31 August 2021

Revision as of 12:34, 31 August 2021

Line 70:

The graph of a function is contained in a [[Cartesian product]] of sets. An <math>X</math>–<math>Y</math> plane is a Cartesian product of two lines, called <math>X</math> and <math>Y,</math> while a cylinder is a cartesian product of a line and a circle, whose height, radius, and angle assign precise locations of the points. [[Fibre bundle]]s are not Cartesian products, but appear to be up close. There is a corresponding notion of a graph on a fibre bundle called a [[Section (fiber bundle)|section]].

The {{visible anchor|graph of a multifunction}}, say the [[multifunction]], <math>\mathcal{R} : X \rightrightarrows Y,</math> is the set <math>\operatorname{gr} \mathcal{R} := \left\{ (x, y) \in X \times Y : y \in \mathcal{R}(x) \right\}.</math>

== See also ==