I've read a bit about the Hawaiian earring and some of its properties. I have a few questions that I haven't been able to find online or derive myself.
- How would we prove that the Hawaiian earring is connected.
- I'm not too familiar with the different types of connectedness. I've only learned about connectedness (with open disjoint separations) and path connectedness. Is the Hawaiian earring path-connected?
- Is there a homeomorphism between the entire Hawaiian earring and the half with only the circles with centers on positive x values?
Edit: I had a slight misunderstanding about the earring but that's been clarified in the comments so 1 and 2 are no longer necessary. I am still curious about number 3, though.