Understanding the definition of domain in Complex Analysis
I have a definition in my book which states, "a nonempty open set that is
connected is called a domain." I understand what an open set is (a set
containing none of its boundary points and I know what a boundary point
is). I am a bit confused with the definition of connected.
Ex. |z-3+2i| $\ge$ 1. We can translate this to (x-3)^2+(y+2)^2 $\ge$ 1. Is
this not a domain because this set contains the boundary points of the
circle centered at (3,-2)?
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