The map which assigns every member of a set 
to the same element 
. It is identical to the identity
function.
Identity Map
See also
Donkin's Theorem, Identity Function, Zero MapExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Identity Map." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IdentityMap.html