Why isn't a homeomorphism, where and is unit circle on the plane?
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What is ?
The book says that is the unit circle on the plane.
Intuitively it says that you cant unwrap the unit circle onto the interval . But you can wrap the interval onto the unit circle. Why is this?
You do realize that for to be a homeomorphic it must be bicontinuous?
That is, both and must be continuous.
Yes I do. Then is not continuous?
What would even be?
Wait, I think is not continuous. Thats why. Something about how the points dont converge to 0 but instead.
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