Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Really stumped on this problem. How should I go about showing that the earrings are connected? Just claim that a circle is connected?

To show it is path connected, we need to cook up a function that maps an interval to the circle, right?

share|improve this question
Your path from one point $x$ to another can go around the circle you start on to the common point, and then along the circle of the other point $y$ of the earring space. –  coffeemath Nov 14 '12 at 4:26
And note that path-connectedness implies connectedness. –  Brian M. Scott Nov 14 '12 at 4:36
to prove path connectedness what function would you use. Motivate the proof for me, if you can Brian. For some reason, I am having a lot of trouble visualizing it. –  user43901 Nov 15 '12 at 1:18

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.