Suppose you have a complex number . Then, an open of radius and center is defined as This essentially means that an open ball of radius centered at contains all complex numbers within this radius.
For a set :
S is if for every there exists some non-zero so that a ball of radius is a subset of this set.
A complex number belongs to the of if there exists some radius for which there is some ball of that radius whose intersection with is not empty.
The set is defined as the of .
The set is closed if it's the same as its closure:
The set is defined as the
A point is an if there is a ball in that contains infinitely many points.