# Simply connected domains

## Homework Statement

http://imageshack.us/photo/my-images/15/unledflsq.png/

## Homework Equations

A simply connected domain D in the complex plane is an open and path
connected set such that every simple closed path in D encloses only points of D.

## The Attempt at a Solution

The answers are a,c and d.I don't understand why they all aren't simply connected. They are all path connected and open. Am I misunderstanding the definition of open?

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Deveno

## Homework Statement

http://imageshack.us/photo/my-images/15/unledflsq.png/

## Homework Equations

A simply connected domain D in the complex plane is an open and path
connected set such that every simple closed path in D encloses only points of D.

## The Attempt at a Solution

The answers are a,c and d.I don't understand why they all aren't simply connected. They are all path connected and open. Am I misunderstanding the definition of open?
consider the following path in (b):

p(t) = (3/2)(cos(2πt) + i sin(2πt)). does that enclose "only points of D"?

Dick
Homework Helper
There's a path in the annulus in b that encloses the origin z=0. What is it? Is z=0 in the annulus?

Deveno
There's a path in the annulus in b that encloses the origin z=0. What is it? Is z=0 in the annulus?
there's a lot of such paths. even discounting homotopic ones, there's still an infinite number.

Dick
Homework Helper
there's a lot of such paths. even discounting homotopic ones, there's still an infinite number.
I know. I was just asking Applejacks to give me one.

Deveno