Thread: Complex Variables (Analysis) HELPPPPPP

Can someone PLEASE help me. I cannot get to where I need to go with this and I am ready to scream.

TIA

Let S be a non-empty set of complex numbers. Show that if S contains all of its accumulation points, then its compliment is open.


I know what it means to be an accumulation point and open set, etc... but for some reason.... I can;t figure this out.

Originally Posted by ginafara

Let S be a non-empty set of complex numbers. Show that if S contains all of its accumulation points, then its compliment is open.

The complement is open if and only if S is closed. Thus, it is sufficient to prove that S is a closed set.