is a circle a connected set?

sketch the sets of points determined by$$|z+2-i|=2$$

is this region:
open, closed or neither.
bounded or unbounded
connected or not connected?

Question

is a circle a connected set?

sketch the sets of points determined by$$|z+2-i|=2$$

is this region:
 open, closed or neither.
bounded or unbounded
connected or not connected?

richyw · Answer

$$|z-(-2+i)|=2$$So I have drawn S as a circle with centre (-2,i) and radius 2.

I think it is neither closed nor open, because and neighborhood of a point on z would be mostly outside S, but also have two points in S.

I said it was bounded because it is contained in a circle centred at the origin.

but I have no idea if it is a connected set. I don't think you can connect any two points with a finite number of straight lines, because a circle is like an infinite number of lines...

richyw · Answer

oops, it would be closed, because it contains all of its boundary.

anonymous · Answer

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How many lines can you draw connecting $z_1$ and $z_2$?

richyw · Answer

uh one?

richyw · Answer

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