Q:

Describe the quotient space $Y=S'/((1,0)\sim(0,-1)\sim(0,1)\sim(-1,0))$

Describe the quotient space $Y=S'/((1,0)\sim(0,-1)\sim(0,1)\sim(-1,0))$
$S'$ be the unit circle in $R^2$
I just simply cant visualise this space 
also how do i check if its connected or compact?
any help greatly appreciated.
I am following Munkres topology and no examples like this or anything similar, completely stuck.

A:

You have taken the circle and decided to consider four points interchangeable.  It doesn't matter what four points they are.  You can think of pushing each one in to the center so they are all $(0,0)$ and you have a four petal flower.   Each petal comes from one quadrant of the circle.  A sketch:  

