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

2. A constant map between topological spaces is continuous.

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