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  20130322 13:57:35 
Last modified on  20130322 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 