# constant function

Definition Suppose $X$ and $Y$ are sets and $f:X\to Y$ is a function. Then $f$ is a constant function if $f(a)=f(b)$ for all $a,b$ in $X$.

## 0.0.1 Properties

1. 1.

The composition of a constant function with any function (for which composition is defined) is a constant function.

2. 2.
 Title constant function Canonical name ConstantFunction Date of creation 2013-03-22 13:57:35 Last modified on 2013-03-22 13:57:35 Owner mathcam (2727) Last modified by mathcam (2727) Numerical id 5 Author mathcam (2727) Entry type Definition Classification msc 03E20 Synonym constant function Synonym constant map Synonym constant mapping Related topic Function Related topic HomotopyOfMaps Related topic ZeroMap