/sci/ - Science & Math

Does a "conformal map" retain any meaning in a strictly real setting? My professor wants us to prove or disprove a conformal surjective map from the the unit ball at the origin in R3 to (x,y,z) in R3 such that z>0. Both are open and simply connected in R3 (same cardinality) so there should be a homeomorphism, but it would need to be something clever to "break" the boundedness of the ball.

I'm tempted to translate by z-1 (a real z), slice along all θ meridians and then do a Mobius transformation (and a rigid motion if needed) to get the circle onto the UHP for that slice of the sphere. I'm not sure how to implement this...the domain is real.

Math is the written, in it's entirety, in a book. The Supreme Fascist keeps the book under lock and key. I don't know why it works, but I bet it's at the end of the book.

>>2604434

Number theory is uncountably gay.

Scifags can't teapot.