The punctured plane is the complex plane 
with the origin removed, i.e.,
. The punctured plane is sometimes
denoted 
(although this notation conflicts with that for the Riemann
sphere C*, or extended complex plane).
Under multiplication, it is an Abelian
group and a Lie group.
Punctured Plane
See also
C*, Complex Plane, Punctured Set, Riemann SphereExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Punctured Plane." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PuncturedPlane.html