topology of the complex plane (original) (raw)

If we identify ℝ2 and ℂ, it is clear that the above topology coincides with topology induced by the Euclidean metric on ℝ2.

Some basic topological concepts for ℂ:

2. 1. A point ζ is an accumulation point of a subset A of ℂ, if any open disk Br⁢(ζ) contains at least one point of A distinct from ζ.
3. 1. A point ζ is an interior point of the set A, if there exists an open disk Br⁢(ζ) which is contained in A.
4. 1. A set A is open, if each of its points is an interior point of A.
5. 1. A set A is closed, if all its accumulation points belong to A.
6. 1. A set A is bounded, if there is an open disk Br⁢(ζ) containing A.
7. 1. A set A is compact, if it is closed and bounded.