- #1

Raziel2701

- 128

- 0

## Homework Statement

Let [tex]U = \{z \in {\mathbb C} | 0<|z|<1\}[/tex] Prove that U is an open set.

## The Attempt at a Solution

I believe I have to use a tool known as the neighborhood or something:

[tex]\left|z - z_0\right|<\epsilon[/tex]

Considering the boundaries, which just by looking at the set it seems to me that since they are not included then the set is open but how do I prove that? Anyway, looking at the boundaries, I'm thinking that I must go and pick some numbers such that the whole mess above with z -z_0 must be less than an epsilon, but that's as far as I go. How do I go about proving the set is open?