# 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.

• Could you define $S'$? Or is this is a typo, and is it supposed to be the 1-sphere $S^1$? – B. Pasternak May 25 '16 at 19:32
• In that case, you have just identified these 4 points on the circle..can you try and imagine what this will look like? Try doing it point per point: pick for example (1,0) and identify (0,1) with this point, and so on. What do you get? – B. Pasternak May 25 '16 at 19:45

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: