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lmedin02
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Homework Statement
Given S1={(x,y) in R2: x2+y2=1}. Show that S1 is a 1-dimensional manifold.
Homework Equations
The Attempt at a Solution
Let f1:(-1,1)->S1 s.t. f1(x)=(x,(1-x2)1/2).
This mapping is a diffeomorphism from (-1,1) onto the top half of the circle S1.
I was trying to write a prove that f1 is indeed a diffeomorphism, but I am having trouble showing the onto part.
I argued that f1 is onto by defining the inverse map and showing that the inverse map is 1 to 1 and hence f1 is onto.