Find some diffeomorphism $A$ on $B$: $$ A=\left\{(x,y)\in \mathbb R^2: x>0, y>0, xy<1 \right\}$$ $$ B=\left\{(x,y)\in \mathbb R^2: 1<x^2+y^2<4, y>0 \right\}$$
I completely do not know how to go about such tasks, because I do not understand diffeomorphism. Could anyone give me some tips?
both are diffeomorphic to the open quarter disc $x>0, y>0, x^2 + y^2 < 1.$ There are explicit smooth mappings that do this. It is crucial that the two sets do not contain their boundary points; all the inequalities use $>$ or $<,$ not $\geq$ or $\leq.$
Still, you ought to do a bunch of easier (but similar) problems before banging your head on this one.
