16 - Topological Notions

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.